theoretical physicist Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experime ...

Lucasian Professor of Mathematics The Lucasian Chair of Mathematics () is a mathematics professorship in the University of Cambridge, England; its holder is known as the Lucasian Professor. The post was founded in 1663 by Henry Lucas, who was Cambridge University's Member of Pa ...

University of Cambridge The University of Cambridge is a public collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III in 1231, Cambridge is the world's third oldest surviving university and one of its most pr ...

University of Miami The University of Miami (UM, UMiami, Miami, U of M, and The U) is a private research university in Coral Gables, Florida. , the university enrolled 19,096 students in 12 colleges and schools across nearly 350 academic majors and programs, i ...

Nobel Prize The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...

quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...

Dirac equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac par ...

antimatter In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter. Antimatter occurs in natural processes like cosmic ray collisions and some types of radioac ...

Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...

Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theo ...

atomic theory Atomic theory is the scientific theory that matter is composed of particles called atoms. Atomic theory traces its origins to an ancient philosophical tradition known as atomism. According to this idea, if one were to take a lump of matter ...

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

Paul Ehrenfest Paul Ehrenfest (18 January 1880 – 25 September 1933) was an Austrian theoretical physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition a ...

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...

Compton effect Compton scattering, discovered by Arthur Holly Compton, is the scattering of a high frequency photon after an interaction with a charged particle, usually an electron. If it results in a decrease in energy (increase in wavelength) of the photon ...

Bristol Bristol () is a city, ceremonial county and unitary authority in England. Situated on the River Avon, it is bordered by the ceremonial counties of Gloucestershire to the north and Somerset to the south. Bristol is the most populous city in ...

Saint-Maurice, Switzerland Saint-Maurice is a city in the Swiss canton of Valais and the capital of the district of Saint-Maurice. On 1 January 2013, the former municipality of Mex merged into the municipality of Saint-Maurice.Cornish

Methodist Methodism, also called the Methodist movement, is a group of historically related denominations of Protestant Christianity whose origins, doctrine and practice derive from the life and teachings of John Wesley. George Whitefield and John's ...

family in

Liskeard Liskeard ( ; kw, Lyskerrys) is a small ancient stannary and market town in south-east Cornwall, South West England. It is situated approximately 20 miles (32 km) west of Plymouth, west of the Devon border, and 12 miles (20 km) eas ...

,

Cornwall Cornwall (; kw, Kernow ) is a historic county and ceremonial county in South West England. It is recognised as one of the Celtic nations, and is the homeland of the Cornish people. Cornwall is bordered to the north and west by the Atlantic ...

. She was named after

Florence Nightingale Florence Nightingale (; 12 May 1820 – 13 August 1910) was an English social reformer, statistician and the founder of modern nursing. Nightingale came to prominence while serving as a manager and trainer of nurses during the Crimean War, i ...

by her father, a ship's captain, who had met Nightingale while he was a soldier during the Crimean war. His mother moved to Bristol as a young woman, where she worked as a librarian at the

Bristol Central Library Bristol Central Library is a historic building on the south side of College Green, Bristol, England. It contains the main collections of Bristol's public library. Built in 1906 by Charles Holden, its design was influential in the development ...

; despite this she still considered her identity to be Cornish rather than English. Paul had a younger sister, Béatrice Isabelle Marguerite, known as Betty, and an older brother, Reginald Charles Félix, known as Felix, who died by suicide in March 1925. Dirac later recalled: "My parents were terribly distressed. I didn't know they cared so much ... I never knew that parents were supposed to care for their children, but from then on I knew." Charles and the children were officially Swiss nationals until they became naturalised on 22 October 1919. Dirac's father was strict and authoritarian, although he disapproved of corporal punishment. Dirac had a strained relationship with his father, so much so that after his father's death, Dirac wrote, "I feel much freer now, and I am my own man." Charles forced his children to speak to him only in French so that they might learn the language. When Dirac found that he could not express what he wanted to say in French, he chose to remain silent.

Education

Dirac was educated first at

Bishop Road Primary School Bishop Road Primary School is a primary school in Bristol, England. It is on Bishop Road in the Bishopston area of Bristol. The school opened in 1896. It is the largest primary school in Bristol, notable for having educated Cary Grant and Paul ...

and then at the all-boys Merchant Venturers' Technical College (later

Cotham School Cotham School is a secondary school with academy status in Cotham, a suburb of Bristol, England. The catchment area for this school is Cotham, Clifton, Kingsdown ,southern Redland, Bishopston, St Paul’s and Easton The school shares a sixth fo ...

), where his father was a French teacher. The school was an institution attached to the

University of Bristol , mottoeng = earningpromotes one's innate power (from Horace, ''Ode 4.4'') , established = 1595 – Merchant Venturers School1876 – University College, Bristol1909 – received royal charter , type ...

, which shared grounds and staff. It emphasised technical subjects like bricklaying, shoemaking and metalwork, and modern languages. This was unusual at a time when secondary education in Britain was still dedicated largely to the classics, and something for which Dirac would later express his gratitude. Dirac studied electrical engineering on a City of Bristol University Scholarship at the University of Bristol's engineering faculty, which was co-located with the Merchant Venturers' Technical College. Shortly before he completed his degree in 1921, he sat for the entrance examination for St John's College, Cambridge. He passed and was awarded a £70 scholarship, but this fell short of the amount of money required to live and study at Cambridge. Despite his having graduated with a

first class honours The British undergraduate degree classification system is a grading structure for undergraduate degrees or bachelor's degrees and integrated master's degrees in the United Kingdom. The system has been applied (sometimes with significant variati ...

Bachelor of Science degree in engineering, the economic climate of the post-war depression was such that he was unable to find work as an engineer. Instead, he took up an offer to study for a

Bachelor of Arts Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four year ...

degree in mathematics at the University of Bristol free of charge. He was permitted to skip the first year of the course owing to his engineering degree. In 1923, Dirac graduated, once again with first class honours, and received a £140 scholarship from the

Department of Scientific and Industrial Research Department of Scientific and Industrial Research, abbreviated DSIR was the name of several British Empire organisations founded after the 1923 Imperial Conference to foster intra-Empire trade and development. * Department of Scientific and Industria ...

. Along with his £70 scholarship from St John's College, this was enough to live at Cambridge. There, Dirac pursued his interests in the theory of

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

, an interest he had gained earlier as a student in Bristol, and in the nascent field of quantum physics, under the supervision of Ralph Fowler. From 1925 to 1928 he held an

1851 Research Fellowship The 1851 Research Fellowship is a scheme conducted by the Royal Commission for the Exhibition of 1851 to annually award a three-year research scholarship to approximately eight "young scientists or engineers of exceptional promise". The fellowship ...

from the

Royal Commission for the Exhibition of 1851 The Royal Commission for the Exhibition of 1851 is an institution founded in 1850 to administer the international exhibition of 1851, officially called the Great Exhibition of the Works of Industry of all Nations. The Great Exhibition was held ...

.1851 Royal Commission Archives He completed his PhD in June 1926 with the first thesis on quantum mechanics to be submitted anywhere. He then continued his research in

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

and

Göttingen Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911. General information The ori ...

. In the spring of 1929, he was a visiting professor at the

University of Wisconsin–Madison A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United Stat ...

.

Family

In 1937, Dirac married Margit Wigner, a sister of physicist

Eugene Wigner Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his co ...

and a divorcee. Dirac raised Margit's two children, Judith and

Gabriel In Abrahamic religions ( Judaism, Christianity and Islam), Gabriel (); Greek: grc, Γαβριήλ, translit=Gabriḗl, label=none; Latin: ''Gabriel''; Coptic: cop, Ⲅⲁⲃⲣⲓⲏⲗ, translit=Gabriêl, label=none; Amharic: am, ገብ ...

, as if they were his own. Paul and Margit Dirac also had two daughters together, Mary Elizabeth and Florence Monica. Margit, known as Manci, had visited her brother in 1934 in

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

, from their native Hungary and, while at dinner at the Annex Restaurant, met the "lonely-looking man at the next table". This account from a Korean physicist, Y. S. Kim, who met and was influenced by Dirac, also says: "It is quite fortunate for the physics community that Manci took good care of our respected Paul A. M. Dirac. Dirac published eleven papers during the period 1939–46... Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else".

Personality

Dirac was known among his colleagues for his precise and taciturn nature. His colleagues in Cambridge jokingly defined a unit called a "dirac", which was one word per hour. When

Niels Bohr Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922 ...

complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it." He criticised the physicist

J. Robert Oppenheimer J. Robert Oppenheimer (; April 22, 1904 – February 18, 1967) was an American theoretical physicist. A professor of physics at the University of California, Berkeley, Oppenheimer was the wartime head of the Los Alamos Laboratory and is oft ...

's interest in poetry: "The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible." Dirac himself wrote in his diary during his postgraduate years that he concentrated solely on his research, and stopped only on Sunday when he took long strolls alone. An anecdote recounted in a review of the 2009 biography tells of

Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent serie ...

and Dirac sailing on an ocean liner to a conference in Japan in August 1929. "Both still in their twenties, and unmarried, they made an odd couple. Heisenberg was a ladies' man who constantly flirted and danced, while Dirac—'an Edwardian geek', as biographer Graham Farmelo puts it—suffered agonies if forced into any kind of socializing or small talk. 'Why do you dance?' Dirac asked his companion. 'When there are nice girls, it is a pleasure,' Heisenberg replied. Dirac pondered this notion, then blurted out: 'But, Heisenberg, how do you know beforehand that the girls are nice? Margit Dirac told both

George Gamow George Gamow (March 4, 1904 – August 19, 1968), born Georgiy Antonovich Gamov ( uk, Георгій Антонович Гамов, russian: Георгий Антонович Гамов), was a Russian-born Soviet and American polymath, theoret ...

and Anton Capri in the 1960s that her husband had said to a house visitor, "Allow me to present Wigner's sister, who is now my wife." Another story told of Dirac is that when he first met the young

Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfl ...

at a conference, he said after a long silence, "I have an equation. Do you have one too?" After he presented a lecture at a conference, one colleague raised his hand and said: "I don't understand the equation on the top-right-hand corner of the blackboard". After a long silence, the moderator asked Dirac if he wanted to answer the question, to which Dirac replied: "That was not a question, it was a comment." Dirac was also noted for his personal modesty. He called the equation for the

time evolution Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called ''stateful systems''). In this formulation, ''time'' is not required to be a continuous parameter, but may be disc ...

of a quantum-mechanical operator, which he was the first to write down, the "Heisenberg equation of motion". Most physicists speak of Fermi–Dirac statistics for half-integer-spin particles and

Bose–Einstein statistics In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic ...

for integer-spin particles. While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Bose statistics" for reasons, he explained, of "symmetry".

Views on religion

Heisenberg recollected a conversation among young participants at the 1927

Solvay Conference The Solvay Conferences (french: Conseils Solvay) have been devoted to outstanding preeminent open problems in both physics and chemistry. They began with the historic invitation-only 1911 Solvay Conference on Physics, considered a turning point i ...

about Einstein and

Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical p ...

's views on religion between

Wolfgang Pauli Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics ...

, Heisenberg and Dirac. Dirac's contribution was a criticism of the political purpose of religion, which Bohr regarded as quite lucid when hearing it from Heisenberg later. Among other things, Dirac said:

I cannot understand why we idle discussing religion. If we are honest—and scientists have to be—we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as to why God allows so much misery and injustice, the exploitation of the poor by the rich, and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards—in heaven if not on earth—all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins.

Heisenberg's view was tolerant. Pauli, raised as a Catholic, had kept silent after some initial remarks, but when finally he was asked for his opinion, said: "Well, our friend Dirac has got a religion and its guiding principle is 'There is no God, and Paul Dirac is His prophet. Everybody, including Dirac, burst into laughter. Later in life, Dirac's views towards the idea of God were less acerbic. As an author of an article appearing in the May 1963 edition of ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it ...

'', Dirac wrote:

It seems to be one of the fundamental features of nature that fundamental
physical law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...
s are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

In 1971, at a conference meeting, Dirac expressed his views on the existence of God. Dirac explained that the existence of God could be justified only if an improbable event were to have taken place in the past:

It could be that it is extremely difficult to start life. It might be that it is so difficult to start a life that it has happened only once among all the planets... Let us consider, just as a conjecture, that the chance of life starting when we have got suitable physical conditions is 10⁻¹⁰⁰. I don't have any logical reason for proposing this figure, I just want you to consider it as a possibility. Under those conditions ... it is almost certain that life would not have started. And I feel that under those conditions it will be necessary to assume the existence of a god to start off life. I would like, therefore, to set up this connection between the existence of a god and the physical laws: if physical laws are such that to start off life involves an excessively small chance so that it will not be reasonable to suppose that life would have started just by blind chance, then there must be a god, and such a god would probably be showing his influence in the quantum jumps which are taking place later on. On the other hand, if life can start very easily and does not need any divine influence, then I will say that there is no god.

Dirac did not commit himself to any definite view, but he described the possibilities for scientifically answering the question of God.

Career

Dirac established the most general theory of quantum mechanics and discovered the relativistic equation for the electron, which now bears his name. The remarkable notion of an antiparticle to each fermion particle – e.g. the positron as antiparticle to the electron – stems from his equation. He was the first to develop quantum field theory, which underlies all theoretical work on sub-atomic or "elementary" particles today, work that is fundamental to our understanding of the forces of nature. He proposed and investigated the concept of a

magnetic monopole In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magneti ...

, an object not yet known empirically, as a means of bringing even greater symmetry to

James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and li ...

's equations of

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...

.

Quantum theory

Dirac's first step into a new quantum theory was taken late in September 1925. Ralph Fowler, his research supervisor, had received a proof copy of an exploratory paper by

Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent serie ...

in the framework of the old quantum theory of Bohr and Sommerfeld. Heisenberg leaned heavily on Bohr's correspondence principle but changed the equations so that they involved directly observable quantities, leading to the matrix formulation of quantum mechanics. Fowler sent Heisenberg's paper on to Dirac, who was on vacation in Bristol, asking him to look into this paper carefully. Dirac's attention was drawn to a mysterious mathematical relationship, at first sight unintelligible, that Heisenberg had established. Several weeks later, back in Cambridge, Dirac suddenly recognised that this mathematical form had the same structure as the Poisson brackets that occur in the

classical dynamics In classical mechanics, analytical dynamics, also known as classical dynamics or simply dynamics, is concerned with the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies, ...

of particle motion. At the time, his memory of Poisson brackets was rather vague, but he found

E. T. Whittaker Sir Edmund Taylor Whittaker (24 October 1873 – 24 March 1956) was a British mathematician, physicist, and historian of science. Whittaker was a leading mathematical scholar of the early 20th-century who contributed widely to applied mathema ...

's ''

Analytical Dynamics of Particles and Rigid Bodies ''A Treatise on the Analytical Dynamics of Particles and Rigid Bodies'' is a treatise and textbook on analytical dynamics by British mathematician Sir Edmund Taylor Whittaker. Initially published in 1904 by the Cambridge University Press, the ...

'' illuminating. From his new understanding, he developed a quantum theory based on non-commuting dynamical variables. This led him to the most profound and significant general formulation of quantum mechanics to date. Dirac's formulation allowed him to obtain the quantisation rules in a novel and more illuminating manner. For this work, published in 1926, Dirac received a PhD from Cambridge. This formed the basis for Fermi-Dirac statistics that applies to systems consisting of many identical spin 1/2 particles (i.e. that obey the

Pauli exclusion principle In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulat ...

), e.g. electrons in solids and liquids, and importantly to the field of conduction in semi-conductors. Dirac was famously not bothered by issues of interpretation in quantum theory. In fact, in a paper published in a book in his honour, he wrote: "The interpretation of quantum mechanics has been dealt with by many authors, and I do not want to discuss it here. I want to deal with more fundamental things."

The Dirac equation

In 1928, building on 2×2 spin matrices which he purported to have discovered independently of

Wolfgang Pauli Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics ...

's work on non-relativistic spin systems (Dirac told

Abraham Pais Abraham Pais (; May 19, 1918 – July 28, 2000) was a Dutch-American physicist and science historian. Pais earned his Ph.D. from University of Utrecht just prior to a Nazi ban on Jewish participation in Dutch universities during World War II. ...

, "I believe I got these atricesindependently of Pauli and possibly Pauli got these independently of me."), he proposed the

Dirac equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac par ...

as a relativistic

equation of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...

for the

wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...

of the

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

. This work led Dirac to predict the existence of the positron, the electron's

antiparticle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...

, which he interpreted in terms of what came to be called the ''

Dirac sea The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by th ...

''. The positron was observed by Carl Anderson in 1932. Dirac's equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon. The necessity of fermions (matter) being created and destroyed in Enrico Fermi's 1934 theory of

beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...

led to a reinterpretation of Dirac's equation as a "classical"

field equation In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equ ...

for any

point particle A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up ...

of spin '' ħ''/2, itself subject to quantisation conditions involving anti-commutators. Thus reinterpreted, in 1934 by

Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent serie ...

, as a (quantum) field equation accurately describing all elementary matter particles – today quarks and leptons – this Dirac field equation is as central to theoretical physics as the Maxwell, Yang–Mills and Einstein field equations. Dirac is regarded as the founder of

quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...

, being the first to use that term. He also introduced the idea of vacuum polarisation in the early 1930s. This work was key to the development of quantum mechanics by the next generation of theorists, in particular Schwinger, Feynman, Sin-Itiro Tomonaga and

Dyson Dyson may refer to: * Dyson (surname), people with the surname Dyson * Dyson (company), a Singaporean multinational home appliances company founded by James Dyson * Dyson (crater), a crater on the Moon * Dyson (operating system), a Unix general-pur ...

in their formulation of quantum electrodynamics. Dirac's ''The'' ''Principles of Quantum Mechanics'', published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of

Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent serie ...

on

matrix mechanics Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum j ...

and of

Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theo ...

on

wave mechanics Wave mechanics may refer to: * the mechanics of waves * the ''wave equation'' in quantum physics, see Schrödinger equation See also * Quantum mechanics * Wave equation The (two-way) wave equation is a second-order linear partial different ...

into a single mathematical formalism that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system. The book also introduced the Dirac delta function. Following his 1939 article, he also included the bra–ket notation in the third edition of his book, thereby contributing to its universal use nowadays.

Magnetic monopoles

In 1931, Dirac proposed that the existence of a single magnetic monopole in the universe would suffice to explain the quantisation of electrical charge. In 1975, 1982 and 2009, intriguing results suggested the possible detection of magnetic monopoles, but there is, to date, no direct evidence for their existence (see also Searches for magnetic monopoles).

Gravity

He quantized the gravitational field and developed a general theory of the

quantum field In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles ...

with dynamical constraints, which forms the basis of the

gauge theories In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie group ...

and superstring theories of today. The influence and importance of Dirac's work have increased with the decades, and physicists use the concepts and equations that he developed daily.

University of Cambridge

Dirac was the

Lucasian Professor of Mathematics The Lucasian Chair of Mathematics () is a mathematics professorship in the University of Cambridge, England; its holder is known as the Lucasian Professor. The post was founded in 1663 by Henry Lucas, who was Cambridge University's Member of Pa ...

at the

University of Cambridge The University of Cambridge is a public collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III in 1231, Cambridge is the world's third oldest surviving university and one of its most pr ...

from 1932 to 1969. In 1937, he proposed a speculative

cosmological Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...

model based on the so-called large numbers hypothesis. During World War II, he conducted important theoretical and experimental research on

uranium enrichment Enriched uranium is a type of uranium in which the percent composition of uranium-235 (written 235U) has been increased through the process of isotope separation. Naturally occurring uranium is composed of three major isotopes: uranium-238 (238 ...

by

gas centrifuge A gas centrifuge is a device that performs isotope separation of gases. A centrifuge relies on the principles of centrifugal force accelerating molecules so that particles of different masses are physically separated in a gradient along the radiu ...

. Dirac's

quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...

(QED) made predictions that were – more often than not – infinite and therefore unacceptable. A workaround known as

renormalisation Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similarity, self-similar geometric structures, that are used to treat infinity, infinities arising in calculated ...

was developed, but Dirac never accepted this. "I must say that I am very dissatisfied with the situation", he said in 1975, "because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small – not neglecting it just because it is infinitely great and you do not want it!" His refusal to accept

renormalisation Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similarity, self-similar geometric structures, that are used to treat infinity, infinities arising in calculated ...

resulted in his work on the subject moving increasingly out of the mainstream. However, from his once rejected notes he managed to work on putting quantum electrodynamics on "logical foundations" based on Hamiltonian formalism that he formulated. He found a rather novel way of deriving the

anomalous magnetic moment In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. (The ''magnetic moment'', also called '' ...

"Schwinger term" and also the

Lamb shift In physics, the Lamb shift, named after Willis Lamb, is a difference in energy between two energy levels 2''S''1/2 and 2''P''1/2 (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which th ...

, afresh in 1963, using the Heisenberg picture and without using the joining method used by Weisskopf and French, and by the two pioneers of modern QED, Schwinger and Feynman. That was two years before the Tomonaga–Schwinger–Feynman QED was given formal recognition by an award of the Nobel Prize for physics. Weisskopf and French (FW) were the first to obtain the correct result for the Lamb shift and the anomalous magnetic moment of the electron. At first FW results did not agree with the incorrect but independent results of Feynman and Schwinger. The 1963–1964 lectures Dirac gave on quantum field theory at

Yeshiva University Yeshiva University is a private Orthodox Jewish university with four campuses in New York City."About YU
on the Yeshiva Universi ...

were published in 1966 as the Belfer Graduate School of Science, Monograph Series Number, 3.

Florida State University and University of Miami

After having relocated to Florida to be near his elder daughter, Mary, Dirac spent his last fourteen years of both life and physics research at the

University of Miami The University of Miami (UM, UMiami, Miami, U of M, and The U) is a private research university in Coral Gables, Florida. , the university enrolled 19,096 students in 12 colleges and schools across nearly 350 academic majors and programs, i ...

in

Coral Gables, Florida Coral Gables, officially City of Coral Gables, is a city in Miami-Dade County, Florida. The city is located southwest of Downtown Miami. As of the 2020 U.S. census, it had a population of 49,248. Coral Gables is known globally as home to the ...

, and Florida State University in

Tallahassee, Florida Tallahassee ( ) is the capital city of the U.S. state of Florida. It is the county seat and only incorporated municipality in Leon County. Tallahassee became the capital of Florida, then the Florida Territory, in 1824. In 2020, the populatio ...

. In the 1950s in his search for a better QED, Paul Dirac developed the Hamiltonian theory of constraints based on lectures that he delivered at the 1949 International Mathematical Congress in Canada. Dirac had also solved the problem of putting the Schwinger–Tomonaga equation into the Schrödinger representation and given explicit expressions for the scalar meson field ( spin zero pion or

pseudoscalar meson In high-energy physics, a pseudoscalar meson is a meson with total spin 0 and odd parity (usually notated as Pseudoscalar mesons are commonly seen in proton-proton scattering and proton-antiproton annihilation, and include the pion (), ...

), the vector meson field (spin one rho meson), and the electromagnetic field (spin one massless boson, photon). The Hamiltonian of constrained systems is one of Dirac's many masterpieces. It is a powerful generalisation of Hamiltonian theory that remains valid for curved spacetime. The equations for the Hamiltonian involve only six degrees of freedom described by

g_

,

p^

for each point of the surface on which the state is considered. The

g_

(''m'' = 0, 1, 2, 3) appear in the theory only through the variables

g^

,

( - ) ^

which occur as arbitrary coefficients in the equations of motion. There are four constraints or weak equations for each point of the surface

x^0

= constant. Three of them

H_r

form the four vector density in the surface. The fourth

H_L

is a 3-dimensional scalar density in the surface ''H''_L ≈ 0; ''H_r'' ≈ 0 (''r'' = 1, 2, 3) In the late 1950s, he applied the Hamiltonian methods he had developed to cast Einstein's general relativity in Hamiltonian form and to bring to a technical completion the quantization problem of gravitation and bring it also closer to the rest of physics according to Salam and DeWitt. In 1959 he also gave an invited talk on "Energy of the Gravitational Field" at the New York Meeting of the American Physical Society. In 1964 he published his ''Lectures on Quantum Mechanics'' (London: Academic) which deals with constrained dynamics of nonlinear dynamical systems including quantization of curved spacetime. He also published a paper entitled "Quantization of the Gravitational Field" in the 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics. From September 1970 to January 1971, Dirac was a Visiting Professor at Florida State University in Tallahassee. During that time he was offered a permanent position there, which he accepted, becoming a full professor in 1972. Contemporary accounts of his time there describe it as happy except that he apparently found the summer heat oppressive and liked to escape from it to Cambridge. He would walk about a mile to work each day and was fond of swimming in one of the two nearby lakes (Silver Lake and Lost Lake), and was also more sociable than he had been at the

University of Cambridge The University of Cambridge is a public collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III in 1231, Cambridge is the world's third oldest surviving university and one of its most pr ...

, where he mostly worked at home apart from giving classes and seminars. At Florida State, he would usually eat lunch with his colleagues before taking a nap. Dirac published over 60 papers in those last twelve years of his life, including a short book on general relativity. His last paper (1984), entitled "The inadequacies of quantum field theory," contains his final judgment on quantum field theory: "These rules of renormalisation give surprisingly, excessively good agreement with experiments. Most physicists say that these working rules are, therefore, correct. I feel that is not an adequate reason. Just because the results happen to be in agreement with observation does not prove that one's theory is correct." The paper ends with the words: "I have spent many years searching for a Hamiltonian to bring into the theory and have not yet found it. I shall continue to work on it as long as I can and other people, I hope, will follow along such lines."

Students

Amongst his many students were Homi J. Bhabha,

Fred Hoyle Sir Fred Hoyle FRS (24 June 1915 – 20 August 2001) was an English astronomer who formulated the theory of stellar nucleosynthesis and was one of the authors of the influential B2FH paper. He also held controversial stances on other sci ...

, John Polkinghorne and

Freeman Dyson Freeman John Dyson (15 December 1923 – 28 February 2020) was an English-American theoretical physicist and mathematician known for his works in quantum field theory, astrophysics, random matrices, mathematical formulation of quantum m ...

. Polkinghorne recalls that Dirac "was once asked what was his fundamental belief. He strode to a blackboard and wrote that the laws of nature should be expressed in beautiful equations."

Honours

Dirac shared the 1933 Nobel Prize for physics with

Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theo ...

"for the discovery of new productive forms of atomic theory". Dirac was also awarded the Royal Medal in 1939 and both the Copley Medal and the

Max Planck Medal The Max Planck medal is the highest award of the German Physical Society , the world's largest organization of physicists, for extraordinary achievements in theoretical physics. The prize has been awarded annually since 1929, with few exceptions, ...

in 1952. He was elected a Fellow of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

in 1930, an Honorary Fellow of the American Physical Society in 1948, and an Honorary Fellow of the

Institute of Physics The Institute of Physics (IOP) is a UK-based learned society and professional body that works to advance physics education, research and application. It was founded in 1874 and has a worldwide membership of over 20,000. The IOP is the Physic ...

, London in 1971. He received the inaugural J. Robert Oppenheimer Memorial Prize in 1969. Dirac became a member of the Order of Merit in 1973, having previously turned down a

knight A knight is a person granted an honorary title of knighthood by a head of state (including the Pope) or representative for service to the monarch, the church or the country, especially in a military capacity. Knighthood finds origins in the Gr ...

hood as he did not want to be addressed by his first name.

Death

In 1984, Dirac died in

Tallahassee, Florida Tallahassee ( ) is the capital city of the U.S. state of Florida. It is the county seat and only incorporated municipality in Leon County. Tallahassee became the capital of Florida, then the Florida Territory, in 1824. In 2020, the populatio ...

, and was buried at Tallahassee's Roselawn Cemetery. Dirac's childhood home in

Bishopston, Bristol Bishopston is a suburb of the city of Bristol in south west England. Bishopston is around Gloucester Road ( A38), the main northern arterial road in the city and Bishop Road. Politics Bishopston is in the Bristol West parliamentary constitue ...

is commemorated with a blue plaque, and the nearby Dirac Road is named in recognition of his links with the city of

Bristol Bristol () is a city, ceremonial county and unitary authority in England. Situated on the River Avon, it is bordered by the ceremonial counties of Gloucestershire to the north and Somerset to the south. Bristol is the most populous city in ...

. A commemorative stone was erected in a garden in

Saint-Maurice, Switzerland Saint-Maurice is a city in the Swiss canton of Valais and the capital of the district of Saint-Maurice. On 1 January 2013, the former municipality of Mex merged into the municipality of Saint-Maurice.slate and inscribed with the

Dirac equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac par ...

, was unveiled in

Westminster Abbey Westminster Abbey, formally titled the Collegiate Church of Saint Peter at Westminster, is an historic, mainly Gothic church in the City of Westminster, London, England, just to the west of the Palace of Westminster. It is one of the Unite ...

. The

Dean of Westminster The Dean of Westminster is the head of the chapter at Westminster Abbey. Due to the Abbey's status as a Royal Peculiar, the dean answers directly to the British monarch (not to the Bishop of London as ordinary, nor to the Archbishop of Canterbu ...

,

Edward Carpenter Edward Carpenter (29 August 1844 – 28 June 1929) was an English utopian socialist, poet, philosopher, anthologist, an early activist for gay rightsWarren Allen Smith: ''Who's Who in Hell, A Handbook and International Directory for Human ...

, had initially refused permission for the memorial, thinking Dirac to be anti-Christian, but was eventually (over a five-year period) persuaded to relent.

Legacy

In 1975, Dirac gave a series of five lectures at the

University of New South Wales The University of New South Wales (UNSW), also known as UNSW Sydney, is a public research university based in Sydney, New South Wales, Australia. It is one of the founding members of Group of Eight, a coalition of Australian research-intensiv ...

which were subsequently published as a book, ''Directions in Physics'' (1978). He donated the royalties from this book to the university for the establishment of the Dirac Lecture Series. The Silver Dirac Medal for the Advancement of Theoretical Physics is awarded by the

University of New South Wales The University of New South Wales (UNSW), also known as UNSW Sydney, is a public research university based in Sydney, New South Wales, Australia. It is one of the founding members of Group of Eight, a coalition of Australian research-intensiv ...

to commemorate the lecture. Immediately after his death, two organizations of professional physicists established annual awards in Dirac's memory. The

Institute of Physics The Institute of Physics (IOP) is a UK-based learned society and professional body that works to advance physics education, research and application. It was founded in 1874 and has a worldwide membership of over 20,000. The IOP is the Physic ...

, the United Kingdom's professional body for physicists, awards the Paul Dirac Medal for "outstanding contributions to theoretical (including mathematical and computational) physics". The first three recipients were Stephen Hawking (1987),

John Stewart Bell John Stewart Bell FRS (28 July 1928 – 1 October 1990) was a physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories. In 2022, the Nobel Prize in Phy ...

(1988), and Roger Penrose (1989). The

International Centre for Theoretical Physics The Abdus Salam International Centre for Theoretical Physics (ICTP) is an international research institute for physical and mathematical sciences that operates under a tripartite agreement between the Italian Government, United Nations Educatio ...

awards the Dirac Medal of the ICTP each year on Dirac's birthday (8 August). The Dirac-Hellman Award at Florida State University was endowed by Bruce P. Hellman in 1997 to reward outstanding work in theoretical physics by FSU researchers. The Paul A.M. Dirac Science Library at Florida State University, which Manci opened in December 1989, is named in his honour, and his papers are held there. Outside is a statue of him by Gabriella Bollobás. The street on which the

National High Magnetic Field Laboratory The National High Magnetic Field Laboratory (MagLab) is a facility at Florida State University, the University of Florida, and Los Alamos National Laboratory in New Mexico, that performs magnetic field research in physics, biology, bioengineering ...

in Innovation Park of Tallahassee, Florida, is located is named Paul Dirac Drive. As well as in his hometown of Bristol, there is also a road named after him, Dirac Place, in

Didcot Didcot ( ) is a railway town and Civil parishes in England, civil parish in the Ceremonial counties of England, ceremonial county of Oxfordshire and the Historic counties of England, historic county of Berkshire. Didcot is south of Oxford, eas ...

, Oxfordshire. The BBC named a

video codec A video codec is software or hardware that compresses and decompresses digital video. In the context of video compression, ''codec'' is a portmanteau of ''encoder'' and ''decoder'', while a device that only compresses is typically called an '' ...

,

Dirac Distributed Research using Advanced Computing (DiRAC) is an integrated supercomputing facility used for research in particle physics, astronomy and cosmology in the United Kingdom. DiRAC makes use of multi-core processors and provides a variety o ...

, in his honour. An asteroid discovered in 1983 was named after Dirac. The Distributed Research utilising Advanced Computing (

DiRAC Distributed Research using Advanced Computing (DiRAC) is an integrated supercomputing facility used for research in particle physics, astronomy and cosmology in the United Kingdom. DiRAC makes use of multi-core processors and provides a variety o ...

) and Dirac software are named in his honour.

Publications

* '' The Principles of Quantum Mechanics'' (1930): This book summarises the ideas of quantum mechanics using the modern formalism that was largely developed by Dirac himself. Towards the end of the book, he also discusses the relativistic theory of the electron (the

Dirac equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac par ...

), which was also pioneered by him. This work does not refer to any other writings then available on quantum mechanics. * ''Lectures on Quantum Mechanics'' (1966): Much of this book deals with quantum mechanics in curved space-time. * ''Lectures on Quantum Field Theory'' (1966): This book lays down the foundations of quantum field theory using the

Hamiltonian Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian ...

formalism. * ''Spinors in Hilbert Space'' (1974): This book based on lectures given in 1969 at the University of Miami, Coral Gables, Florida, USA, deals with the basic aspects of

spinor In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a sligh ...

s starting with a real Hilbert space formalism. Dirac concludes with the prophetic words "We have

boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spi ...

variables appearing automatically in a theory that starts with only fermion variables, provided the number of fermion variables is infinite. There must be such

boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spi ...

variables connected with

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

s..." * ''General Theory of Relativity'' (1975): This 69-page work summarises Einstein's general theory of relativity.

References

Citations

General sources

* * * ublished in the United States as ''The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom''. .* * * * * *

External links

Oral history interview transcript with P. A. M. Dirac on 1 April 1962, American Institute of Physics, Niels Bohr Library & Archives
- Session I
Oral history interview transcript with P. A. M. Dirac on 6 May 1963, American Institute of Physics, Niels Bohr Library & Archives
- Session II
Oral history interview transcript with P. A. M. Dirac on 7 Mary 1963, American Institute of Physics, Niels Bohr Library & Archives
- Session III
Oral history interview transcript with P. A. M. Dirac on 10 May 1963, American Institute of Physics, Niels Bohr Library & Archives
- Session IV
Oral history interview transcript with P. A. M. Dirac on 14 May 1963, American Institute of Physics, Niels Bohr Library & Archives
- V
Free online access to Dirac's classic 1920s papers from Royal Society's Proceedings A

Annotated bibliography for Paul Dirac from the Alsos Digital Library for Nuclear Issues

The Paul Dirac Collection at Florida State University

The Papers of Professor Paul Dirac
at

Churchill Archives Centre The Churchill Archives Centre (CAC) at Churchill College at the University of Cambridge is one of the largest repositories in the United Kingdom for the preservation and study of modern personal papers. It is best known for housing the papers of ...

{{DEFAULTSORT:Dirac, Paul 1902 births 1984 deaths 20th-century British physicists Alumni of St John's College, Cambridge Alumni of the University of Bristol British Nobel laureates British people of Swiss descent English agnostics English emigrants to the United States 20th-century British mathematicians English Nobel laureates Fellows of the Royal Society Florida State University faculty Foreign associates of the National Academy of Sciences Foreign Members of the USSR Academy of Sciences Institute for Advanced Study visiting scholars Lucasian Professors of Mathematics Mathematical physicists Members of the Order of Merit Members of the Pontifical Academy of Sciences Nobel laureates in Physics Quantum physicists Recipients of the Copley Medal Royal Medal winners Scientists from Bristol Theoretical physicists University of Göttingen faculty University of Miami faculty Winners of the Max Planck Medal

Personal life

Early years

Education

Family

Personality

Views on religion

Career

Quantum theory

The Dirac equation

Magnetic monopoles

Gravity

University of Cambridge

Florida State University and University of Miami

Students

Honours

Death

Legacy

Publications

References

Citations

General sources

Further reading

External links