Paul Adrien Maurice Dirac OM FRS (/dɪˈræk/; 8 August 1902 – 20
October 1984) was an English theoretical physicist who is regarded as
one of the most significant physicists of the 20th century.
Dirac made fundamental contributions to the early development of both
quantum mechanics and quantum electrodynamics. Among other
discoveries, he formulated the
Dirac equation which describes the
behaviour of fermions and predicted the existence of antimatter. Dirac
shared the 1933
Nobel Prize in Physics
Nobel Prize in Physics with
Erwin Schrödinger "for
the discovery of new productive forms of atomic theory". He also
made significant contributions to the reconciliation of general
relativity with quantum mechanics.
Dirac was regarded by his friends and colleagues as unusual in
character. In a 1926 letter to Paul Ehrenfest,
Albert Einstein wrote
of Dirac, "This balancing on the dizzying path between genius and
madness is awful".
He was the
Lucasian Professor of Mathematics at the University of
Cambridge, a member of the Center for Theoretical Studies, University
of Miami, and spent the last decade of his life at Florida State
1 Personal life
1.1 Early years
1.5 Religious views
2.3 The Dirac equation
2.4 Magnetic monopoles
2.5 Lucasian Chair
2.6 Professorship at Florida State University
5.2 Further reading
5.3 External links
Paul Adrien Maurice Dirac was born at his parents' home in Bristol,
England, on 8 August 1902, and grew up in the Bishopston area of
the city. His father, Charles Adrien Ladislas Dirac, was an
immigrant from Saint-Maurice, Switzerland, who worked in
Bristol as a
French teacher. His mother, Florence Hannah Dirac, née Holten, the
daughter of a ship's captain, was born in Cornwall, England, and
worked as a librarian at the
Bristol Central Library. Paul had a
younger sister, Béatrice Isabelle Marguerite, known as Betty, and an
older brother, Reginald Charles Félix, known as Felix, who
committed 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, in order that they learn the language. When Dirac found that
he could not express what he wanted to say in French, he chose to
Dirac was educated first at Bishop Road Primary School and then at
the all-boys Merchant Venturers' Technical College (later Cotham
School), where his father was a French teacher. The school was an
institution attached to the University of Bristol, which shared
grounds and staff. It emphasised technical subjects like
bricklaying, shoemaking and metal work, 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
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 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 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 degree in mathematics at the University
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. 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, 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 from the Royal
Commission for the Exhibition of 1851. He completed his PhD in
June 1926 with the first thesis on quantum mechanics to be submitted
anywhere. He then continued his research in
Paul Dirac with his wife in Copenhagen, July 1963
Dirac married Margit Wigner (Eugene Wigner's sister), in 1937. He
adopted Margit's two children, Judith and Gabriel. Paul and Margit
Dirac had two children together, both daughters, Mary Elizabeth and
Margit, known as Manci, visited her brother in 1934 in Princeton, New
Jersey, from her 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."
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 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'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 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
socialising 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?'"
According to a story told in different versions, a friend or student
visited Dirac, not knowing of his marriage. Noticing the visitor's
surprise at seeing an attractive woman in the house, Dirac said, "This
is... this is Wigner's sister". Margit Dirac told both George Gamow
and Anton Capri in the 1960s that her husband had actually said,
"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 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 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
Bose–Einstein statistics for integer-spin particles.
While lecturing later in life, Dirac always insisted on calling the
former "Fermi statistics". He referred to the latter as "Einstein
statistics" for reasons, he explained, of "symmetry".
Heisenberg recollected a conversation among young participants at the
Solvay Conference about Einstein and Planck's views on religion
between Wolfgang Pauli, Heisenberg and Dirac. Dirac's contribution was
a criticism of the political purpose of religion, which was much
appreciated for its lucidity by Bohr when Heisenberg reported it to
him 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 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, Dirac wrote:
It seems to be one of the fundamental features of nature that
fundamental physical laws 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
only be justified if an improbable event were to have taken place in
It could be that it is extremely difficult to start life. It might be
that it is so difficult to start life that it has happened only once
among all the planets... Let us consider, just as a conjecture, that
the chance 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 connexion 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 commend himself to any definite view, but he described
the possibilities for answering the question of God in a scientific
Dirac shared the 1933 Nobel Prize for physics with Erwin Schrödinger
"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
Max Planck Medal in 1952. He was elected a Fellow of the Royal
Society in 1930, an Honorary Fellow of the American Physical
Society in 1948, and an Honorary Fellow of the Institute of Physics,
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 knighthood as he did
not want to be addressed by his first name.
Dirac's grave in Roselawn Cemetery, Tallahassee, Florida. Also buried
is his wife Manci (Margit Wigner). Their daughter Mary Elizabeth
Dirac, who died 20 January 2007, is buried next to them but not shown
in the photograph.
The commemorative marker in Westminster Abbey.
In 1984, Dirac died in Tallahassee, Florida, and was buried at
Tallahassee's Roselawn Cemetery. Dirac's childhood home in
Bristol is commemorated with a blue plaque and the nearby Dirac Road
is named in recognition of his links with the city. A commemorative
stone was erected in a garden in Saint-Maurice, Switzerland, the town
of origin of his father's family, on 1 August 1991. On 13 November
1995 a commemorative marker, made from Burlington green slate and
inscribed with the Dirac equation, was unveiled in Westminster
Abbey. The Dean of Westminster, Edward Carpenter, had
initially refused permission for the memorial, thinking Dirac to be
anti-Christian, but was eventually (over a five-year period) persuaded
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, an object not yet known
empirically, as a means of bringing even greater symmetry to James
Clerk Maxwell's equations of electromagnetism.
He quantised the gravitational field, and developed a general theory
of quantum field theories with dynamical constraints, which forms the
basis of the gauge theories and superstring theories of today. The
influence and importance of his work has increased with the decades,
and physicists use the concepts and equations that he developed daily.
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 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 reached. 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 of particle motion. From this thought
he quickly developed a quantum theory that was based on non-commuting
dynamical variables. This led him to a more profound and significant
general formulation of quantum mechanics than was achieved by any
other worker in this field. 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), e.g. electrons in
solids and liquids, and importantly to the field of conduction in
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
Further information: Dirac equation
In 1928, building on 2×2 spin matrices which he purported to have
discovered independently of Wolfgang Pauli's work on non-relativistic
spin systems (Dirac told Abraham Pais, "I believe I got these
[matrices] independently of Pauli and possibly Pauli got these
independently of me."), he proposed the
Dirac equation as a
relativistic equation of motion for the wave function of the
electron. This work led Dirac to predict the existence of the
positron, the electron's antiparticle, which he interpreted in terms
of what came to be called the Dirac sea. 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 led to a reinterpretation of
Dirac's equation as a "classical" field equation for any point
particle of spin ħ/2, itself subject to quantisation conditions
involving anti-commutators. Thus reinterpreted, in 1934 by Werner
Heisenberg, 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, 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 in their formulation of quantum
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 on
matrix mechanics and of
Erwin Schrödinger on wave mechanics 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 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.
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 Magnetic monopole#Searches for magnetic
Dirac was the
Lucasian Professor of Mathematics at Cambridge from 1932
to 1969. In 1937, he proposed a speculative cosmological model based
on the so-called large numbers hypothesis. During World War II, he
conducted important theoretical and experimental research on uranium
enrichment by gas centrifuge.
Dirac's quantum electrodynamics (QED) made predictions that were –
more often than not – infinite and therefore unacceptable. A
workaround known as renormalisation 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
resulted in his work on the subject moving increasingly out of the
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 "Schwinger term" and also the Lamb
shift, 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
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 were published in
1966 as the Belfer Graduate School of Science, Monograph Series
Number, 3. 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
University of Miami in Coral Gables, Florida,
Florida State University
Florida State University in Tallahassee, Florida.
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
Tomonaga–Schwinger equation into the Schrödinger representation
and given explicit expressions for the scalar meson field (spin zero
pion or pseudoscalar meson), the vector meson field (spin one rho
meson), and the electromagnetic field (spin one massless boson,
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
displaystyle g_ rs
displaystyle p^ rs
for each point of the surface on which the state is considered. The
displaystyle g_ m0
(m = 0, 1, 2, 3) appear in the theory only through the variables
displaystyle g^ r0
displaystyle (- g^ 00 )^ -1/2
which occur as arbitrary coefficients in the equations of motion.
There are four constraints or weak equations for each point of the
displaystyle x^ 0
= constant. Three of them
displaystyle H_ r
form the four vector density in the surface. The fourth
displaystyle H_ L
is a 3-dimensional scalar density in the surface HL ≈ 0; Hr ≈ 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 quantisation 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 later published in 1959 Phys Rev Lett 2, 368. In 1964
he published his Lectures on
Quantum Mechanics (London:Academic) which
deals with constrained dynamics of nonlinear dynamical systems
including quantisation of curved spacetime. He also published a paper
entitled "Quantization of the Gravitational Field" in the 1967
ICTP/IAEA Trieste Symposium on Contemporary Physics.
Professorship at Florida State University
From September 1970 to January 1971, Dirac was Visiting Professor at
Florida State University
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 Cambridge, where he mostly
worked at home apart from giving classes and seminars; at FSU 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 these 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."
(Source: "Paul Dirac: The Man and his Work" by
Abraham Pais et al.)
Amongst his many students were Homi J. Bhabha, Fred Hoyle
and John Polkinghorne. 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
In 1975, Dirac gave a series of five lectures at the University of New
South Wales 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
University of New South Wales to commemorate the
Immediately after his death, two organisations of professional
physicists established annual awards in Dirac's memory. The Institute
of Physics, the United Kingdom's professional body for physicists,
Paul Dirac Medal for "outstanding contributions to
theoretical (including mathematical and computational) physics".
The first three recipients were
Stephen Hawking (1987), John Stewart
Bell (1988), and
Roger Penrose (1989). The International Centre for
Theoretical Physics awards the Dirac Medal of the ICTP each year on
Dirac's birthday (8 August).
The Dirac-Hellman Award at
Florida State University
Florida State University was endowed by Dr
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
National High Magnetic Field Laboratory in Innovation Park of
Tallahassee, Florida, is located is named
Paul Dirac Drive. As well as
in his home town of Bristol, there is also a road named after him in
Didcot Oxfordshire, Dirac Place. The BBC named a video codec,
Dirac, in his honour. An asteroid discovered in 1983 was named after
Dirac. The Distributed Research utilising Advanced Computing
(DiRAC) and Dirac software are named in his honour.
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), which was also pioneered by him. This work does not refer
to any other writings then available on quantum mechanics.
Quantum Mechanics (1966): Much of this book deals with
quantum mechanics in curved space-time.
Quantum Field Theory (1966): This book lays down the
foundations of quantum field theory using the 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 spinors starting with a real Hilbert space
formalism. Dirac concludes with the prophetic words "We have boson
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 variables connected with
General Theory of Relativity (1975): This 69-page work summarises
Einstein's general theory of relativity.
^ "Nobel Bio". Nobelprize.org. Retrieved 27 January 2014.
^ a b Bhabha, Homi Jehangir (1935). On cosmic radiation and the
creation and annihilation of positrons and electrons.
repository.cam.ac.uk (PhD thesis). University of Cambridge.
^ a b
Paul Dirac at the Mathematics Genealogy Project
^ a b Polkinghorne, John Charlton (1955). Contributions to quantum
field theory. lib.cam.ac.uk (PhD thesis). University of Cambridge.
^ Farmelo, Graham (2009). The Strangest Man: The Hidden Life of Paul
Quantum Genius. Faber and Faber. ISBN 9780571222780.
^ Cassidy, David C. (2010). "Graham Farmelo. The Strangest Man: The
Hidden Life of Paul Dirac, Mystic of the Atom". Isis. University of
Chicago Press. 101: 661–661. doi:10.1086/657209. Farmelo also
discusses, across several chapters, the influences of John Stuart
^ a b Dalitz, R. H.; Peierls, R. (1986). "Paul Adrien Maurice Dirac. 8
August 1902 – 20 October 1984". Biographical Memoirs of Fellows of
the Royal Society. 32: 138. doi:10.1098/rsbm.1986.0006.
^ a b "The
Nobel Prize in Physics
Nobel Prize in Physics 1933". The Nobel Foundation.
Retrieved 4 April 2013.
^ Sukumar, N. (2012). A Matter of Density: Exploring the Electron
Density Concept in the Chemical, Biological, and Materials Sciences.
John Wiley & Sons. p. 27. ISBN 9781118431719. Retrieved
3 April 2013.
^ Farmelo 2009, p. 10
^ Farmelo 2009, pp. 18–19
^ Kragh 1990, p. 1
^ Farmelo 2009, pp. 10–11
^ Farmelo 2009, pp. 77–78
^ Farmelo 2009, p. 79
^ Farmelo 2009, p. 34
^ Farmelo 2009, p. 22
^ Mehra 1972, p. 17
^ Kragh 1990, p. 2
^ Farmelo 2009, pp. 13–17
^ Farmelo 2009, pp. 20–21
^ a b Mehra 1972, p. 18
^ Farmelo 2009, p. 23
^ Farmelo 2009, p. 28
^ Farmelo 2009, pp. 46–47
^ Farmelo 2009, p. 53
^ Farmelo 2009, pp. 52–53
^ a b 1851 Royal Commission Archives
^ Farmelo 2009, p. 101
^ Kim, Young Suh (1995). "Wigner's Sisters". Retrieved 4 April
^ Farmelo 2009, p. 89
^ "Paul Adrien Maurice Dirac". University of St. Andrews. Retrieved 4
^ Mehra 1972, pp. 17–59
^ Kragh (1990), p. 17.
^ a b McKie, Rob (1 February 2009). "Anti-matter and madness". The
Guardian. Retrieved 4 April 2013.
^ Gamow 1966, p. 121
^ Capri 2007, p. 148
^ Zee 2010, p. 105
^ Raymo, Chet (17 October 2009). "A quantum leap into oddness". Globe
and Mail. (Review of Farmelo's The Strangest Man.)
^ Farmelo 2009, pp. 161–162, who attributes the story to Niels
^ Mehra, Jagdish; Rechenberg, Helmut (2001). The Historical
Quantum Theory. Springer Science & Business Media.
p. 746. ISBN 9780387951805.
^ Heisenberg 1971, pp. 85–86
^ Heisenberg 1971, p. 87
^ Farmelo 2009, p. 138, who says this was an old joke, pointing
out in a footnote that Punch wrote in the 1850s that "There is no God,
Harriet Martineau is her prophet."
^ Dirac, Paul (May 1963). "The Evolution of the Physicist's Picture of
Nature". Scientific American. Retrieved 4 April 2013.
^ a b c Helge Kragh (1990). "The purest soul". Dirac: A Scientific
Biography. Cambridge University Press. pp. 256–257.
^ Walter, Claire (1982). Winners, the blue ribbon encyclopedia of
awards. Facts on
File Inc. p. 438. ISBN 9780871963864.
^ "Dirac Receives Miami Center Oppenheimer Memorial Prize". Physics
Today. American Institute of Physics: 127. April 1969.
doi:10.1063/1.3035512. Retrieved 1 March 2015.
^ Farmelo 2009, pp. 403–404
^ a b "Dirac takes his place next to Isaac Newton". Florida State
University. Archived from the original on 27 April 1997. Retrieved 4
^ Paul Adrien Maurice Dirac at Find a Grave
^ "Paul Dirac". Gisela Dirac. Retrieved 4 April 2013.
^ Farmelo 2009, pp. 414–15
^ "Paul Dirac: a genius in the history of physics". Cern Courier.
Retrieved 13 May 2013.
^ Dirac, Paul A. M. (1926). "On the Theory of
Proceedings of the
Royal Society A. 112 (762): 661–77.
^ P. A. M. Dirac, The inadequacies of quantum field theory, in Paul
Adrien Maurice Dirac, B. N. Kursunoglu and E. P. Wigner, Eds.
(Cambridge University, Cambridge, 1987) p. 194
^ Behram N. Kursunoglu; Eugene Paul Wigner (eds.). Reminiscences about
a Great Physicist. Cambridge University Press. p. 98.
^ Dirac, P. A. M. (1 February 1928). "The
Quantum Theory of the
Electron". Proceedings of the
Royal Society of London A. 117 (778):
^ Dirac, Paul (12 December 1933). "Theory of electrons and positrons"
(PDF). Nobel Lecture. Retrieved 13 May 2013.
^ P. A. M. Dirac (1939). "A New Notation for
Proceedings of the Cambridge Philosophical Society. 35 (3): 416.
^ Gieres (2000). "Mathematical surprises and Dirac's formalism in
quantum mechanics". Reports on Progress in Physics. 63 (12): 1893.
arXiv:quant-ph/9907069 . Bibcode:2000RPPh...63.1893G.
^ Dirac, P. A. M. (1931). "Quantised Singularities in the
Electromagnetic Field". Proceedings of the
Royal Society A. The Royal
Society. 133: 60–72. Bibcode:1931RSPSA.133...60D.
^ P. B. Price; E. K. Shirk; W. Z. Osborne; L. S. Pinsky (25 August
1975). "Evidence for Detection of a Moving Magnetic Monopole".
Physical Review Letters. American Physical Society. 35 (8): 487–90.
^ Blas Cabrera (17 May 1982). "First Results from a Superconductive
Detector for Moving Magnetic Monopoles". Physical Review Letters.
American Physical Society. 48 (20): 1378–81.
^ "Magnetic Monopoles Detected in a Real Magnet for the First Time".
Science Daily. 4 September 2009. Retrieved 13 May 2013.
^ D.J.P. Morris; D.A. Tennant; S.A. Grigera; B. Klemke; C. Castelnovo;
R. Moessner; C. Czternasty; M. Meissner; K.C. Rule; J.-U. Hoffmann; K.
Kiefer; S. Gerischer; D. Slobinsky & R.S. Perry (3 September
2009). "Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7".
Science. 326 (5951): 411–4. arXiv:1011.1174 .
^ S. T. Bramwell; S. R. Giblin; S. Calder; R. Aldus; D. Prabhakaran;
T. Fennell (15 October 2009). "Measurement of the charge and current
of magnetic monopoles in spin ice". Nature. 461 (7266): 956–9.
arXiv:0907.0956 . Bibcode:2009Natur.461..956B.
doi:10.1038/nature08500. PMID 19829376.
^ Kragh 1990, p. 184
^ Schweber 1994
^ Canad J Math 1950 vol 2, 129; 1951 vol 3, 1
^ 1951 "The Hamiltonian Form of Field Dynamics" Canad Jour Math, vol
^ Phillips R. J. N. 1987 Tributes to Dirac p31 London: Adam Hilger
^ Proc Roy Soc 1958, A vol 246, 333, Phys Rev 1959, vol 114, 924
^ O'Connor, John J.; Robertson, Edmund F., "Paul Dirac", MacTutor
History of Mathematics archive, University of St Andrews .
^ John Polkinghorne. 'Belief in God in an Age of Science' p 2
^ "Dirac Medal awards". University of New South Wales. Archived from
the original on 12 April 2013. Retrieved 4 April 2013.
^ "The Dirac Medal". Institute of Physics. Retrieved 24 November
^ "The Dirac Medal". International Centre for Theoretical Physics.
Retrieved 4 April 2013.
^ "Undergraduate Awards". Florida State University. Archived from the
original on 12 April 2013. Retrieved 4 April 2013.
^ "Remodelled Dirac Science Library Opened at FSU". Graham Farmelo.
Retrieved 12 October 2015.
^ "Paul Adrien Maurice Dirac Collection". Florida State University.
Archived from the original on 15 July 2013. Retrieved 4 April
^ Farmelo 2009, p. 417
5997 Dirac (1983 TH)". Jet Propulsion Laboratory. Retrieved
Capri, Anton Z. (2007). Quips, Quotes, and Quanta: An Anecdotal
History of Physics. Hackensack, New Jersey: World Scientific.
ISBN 981-270-919-3. OCLC 214286147. Retrieved 8 June
Crease, Robert P.; Mann, Charles C. (1986). The Second Creation:
Makers of the Revolution in Twentieth Century Physics. New York City:
Macmillan Publishing. ISBN 0-02-521440-3.
Gamow, George (1966). Thirty Years That Shook Physics: The Story of
Quantum Theory. Garden City, New York: Doubleday.
ISBN 0-486-24895-X. OCLC 11970045. Retrieved 8 June
Heisenberg, Werner (1971). Physics and Beyond: Encounters and
Conversations. New York City: Harper & Row.
ISBN 0-06-131622-9. OCLC 115992.
Kragh, Helge (1990). Dirac: A Scientific Biography. Cambridge:
Cambridge University Press. ISBN 0-521-38089-8.
OCLC 20013981. Retrieved 8 June 2008.
Mehra, Jagdish (1972). "The Golden Age of Theoretical Physics: P. A.
M. Dirac's Scientific Works from 1924–1933". In Wigner, Eugene Paul;
Salam, Abdus. Aspects of
Quantum Theory. Cambridge: University Press.
pp. 17–59. ISBN 0-521-08600-0. OCLC 532357.
Schweber, Silvan S. (1994). QED and the men who made it: Dyson,
Feynman, Schwinger, and Tomonaga. Princeton, New Jersey: Princeton
University Press. ISBN 0-691-03685-3. OCLC 28966591.
Zee, A. (2010).
Quantum Field Theory in a Nutshell. Princeton, New
Jersey: Princeton University Press. ISBN 978-1-4008-3532-4.
Brown, Helen (24 January 2009). "The Strangest Man: The Hidden Life of
Paul Dirac by
Graham Farmelo – review [print version: The man behind
The Daily Telegraph
The Daily Telegraph (Review). p. 20. Retrieved 11
April 2011. .
Gilder, Louisa (13 September 2009). "
Quantum Leap – Review of 'The
Strangest Man: The Hidden Life of
Paul Dirac by Graham Farmelo'". The
New York Times. Retrieved 11 April 2011. Review.
Wikimedia Commons has media related to:
Paul Dirac (category)
Wikiquote has quotations related to: Paul Dirac
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
Paul Dirac Collection at Florida State University
Letters from Dirac (1932–36) and other papers
Oral History interview transcript with Dirac 1 April 1962, 6, 7, 10,
& 14 May 1963, American Institute of Physics,
Niels Bohr Library
Copley Medallists (1951–2000)
David Keilin (1951)
Paul Dirac (1952)
Albert Kluyver (1953)
E. T. Whittaker
E. T. Whittaker (1954)
Ronald Fisher (1955)
Patrick Blackett (1956)
Howard Florey (1957)
John Edensor Littlewood (1958)
Frank Macfarlane Burnet
Frank Macfarlane Burnet (1959)
Harold Jeffreys (1960)
Hans Adolf Krebs
Hans Adolf Krebs (1961)
Cyril Norman Hinshelwood
Cyril Norman Hinshelwood (1962)
Paul Fildes (1963)
Sydney Chapman (1964)
Alan Lloyd Hodgkin
Alan Lloyd Hodgkin (1965)
Lawrence Bragg (1966)
Bernard Katz (1967)
Tadeusz Reichstein (1968)
Peter Medawar (1969)
Alexander R. Todd
Alexander R. Todd (1970)
Norman Pirie (1971)
Nevill Francis Mott (1972)
Andrew Huxley (1973)
W. V. D. Hodge
W. V. D. Hodge (1974)
Francis Crick (1975)
Dorothy Hodgkin (1976)
Frederick Sanger (1977)
Robert Burns Woodward
Robert Burns Woodward (1978)
Max Perutz (1979)
Derek Barton (1980)
Peter D. Mitchell
Peter D. Mitchell (1981)
John Cornforth (1982)
Rodney Robert Porter
Rodney Robert Porter (1983)
Subrahmanyan Chandrasekhar (1984)
Aaron Klug (1985)
Rudolf Peierls (1986)
Robin Hill (1987)
Michael Atiyah (1988)
César Milstein (1989)
Abdus Salam (1990)
Sydney Brenner (1991)
George Porter (1992)
James D. Watson (1993)
Frederick Charles Frank
Frederick Charles Frank (1994)
Frank Fenner (1995)
Alan Cottrell (1996)
Hugh Huxley (1997)
James Lighthill (1998)
John Maynard Smith
John Maynard Smith (1999)
Alan Battersby (2000)
Laureates of the Nobel Prize in Physics
1902 Lorentz / Zeeman
1903 Becquerel / P. Curie / M. Curie
1906 J. J. Thomson
1909 Marconi / Braun
1910 Van der Waals
1913 Kamerlingh Onnes
1915 W. L. Bragg / W. H. Bragg
1922 N. Bohr
1924 M. Siegbahn
1925 Franck / Hertz
1927 Compton / C. Wilson
1928 O. Richardson
1929 De Broglie
1933 Schrödinger / Dirac
1936 Hess / C. D. Anderson
1937 Davisson / G. P. Thomson
1951 Cockcroft / Walton
1952 Bloch / Purcell
1954 Born / Bothe
1955 Lamb / Kusch
1956 Shockley / Bardeen / Brattain
1957 C. N. Yang / T. D. Lee
1958 Cherenkov / Frank / Tamm
1959 Segrè / Chamberlain
1961 Hofstadter / Mössbauer
1963 Wigner / Goeppert-Mayer / Jensen
1964 Townes / Basov / Prokhorov
1965 Tomonaga / Schwinger / Feynman
1970 Alfvén / Néel
1972 Bardeen / Cooper / Schrieffer
1973 Esaki / Giaever / Josephson
1974 Ryle / Hewish
1975 A. Bohr / Mottelson / Rainwater
1976 Richter / Ting
1977 P. W. Anderson / Mott / Van Vleck
1978 Kapitsa / Penzias / R. Wilson
1979 Glashow / Salam / Weinberg
1980 Cronin / Fitch
1981 Bloembergen / Schawlow / K. Siegbahn
1982 K. Wilson
1983 Chandrasekhar / Fowler
1984 Rubbia / Van der Meer
1985 von Klitzing
1986 Ruska / Binnig / Rohrer
1987 Bednorz / Müller
1988 Lederman / Schwartz / Steinberger
1989 Ramsey / Dehmelt / Paul
1990 Friedman / Kendall / R. Taylor
1991 de Gennes
1993 Hulse / J. Taylor
1994 Brockhouse / Shull
1995 Perl / Reines
1996 D. Lee / Osheroff / R. Richardson
1997 Chu / Cohen-Tannoudji / Phillips
1998 Laughlin / Störmer / Tsui
1999 't Hooft / Veltman
2000 Alferov / Kroemer / Kilby
2001 Cornell / Ketterle / Wieman
2002 Davis / Koshiba / Giacconi
2003 Abrikosov / Ginzburg / Leggett
2004 Gross / Politzer / Wilczek
2005 Glauber / Hall / Hänsch
2006 Mather / Smoot
2007 Fert / Grünberg
2008 Nambu / Kobayashi / Maskawa
2009 Kao / Boyle / Smith
2010 Geim / Novoselov
2011 Perlmutter / Riess / Schmidt
2012 Wineland / Haroche
2013 Englert / Higgs
2014 Akasaki / Amano / Nakamura
2015 Kajita / McDonald
2016 Thouless / Haldane / Kosterlitz
2017 Weiss / Barish / Thorne
Lucasian Professors of Mathematics
Isaac Barrow (1664)
Isaac Newton (1669)
William Whiston (1702)
Nicholas Saunderson (1711)
John Colson (1739)
Edward Waring (1760)
Isaac Milner (1798)
Robert Woodhouse (1820)
Thomas Turton (1822)
George Biddell Airy
George Biddell Airy (1826)
Charles Babbage (1828)
Joshua King (1839)
George Stokes (1849)
Joseph Larmor (1903)
Paul Dirac (1932)
James Lighthill (1969)
Stephen Hawking (1979)
Michael Green (2009)
Michael Cates (2015)
History of science
History of science portal
ISNI: 0000 0001 0875 2133
BNF: cb12860605f (data)