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Yang–Mills Theory
In mathematical physics, Yang–Mills theory is a gauge theory based on a special unitary group SU(''N''), or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using these non-abelian Lie groups and is at the core of the unification of the electromagnetic force and weak forces (i.e. U(1) × SU(2)) as well as quantum chromodynamics, the theory of the strong force (based on SU(3)). Thus it forms the basis of our understanding of the Standard Model of particle physics. History and theoretical description In 1953, in a private correspondence, Wolfgang Pauli formulated a six-dimensional theory of Einstein's field equations of general relativity, extending the five-dimensional theory of Kaluza, Klein, Fock and others to a higher-dimensional internal space. However, there is no evidence that Pauli developed the Lagrangian of a gauge field or the quantization of it. Because Pauli found that his theory "lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory (quantum Mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system. Approximate Hamiltonians Perturbation theory is an important tool for de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeffrey Goldstone
Jeffrey Goldstone (born 3 September 1933) is a British theoretical physicist and an ''emeritus'' physics faculty member at the MIT Center for Theoretical Physics. He worked at the University of Cambridge until 1977. He is famous for the discovery of the Nambu–Goldstone boson. He is currently working on quantum computation. Biography Born in Manchester, he was educated at Manchester Grammar School and Trinity College, Cambridge, (B.A. 1954, Ph.D. 1958). He worked on the theory of nuclear matter under the guidance of Hans Bethe and developed modifications of Feynman diagrams for non-relativistic many-fermion systems, which are currently referred to as Goldstone diagrams. Goldstone was a research fellow of Trinity College, Cambridge, from 1956 to 1960 and held visiting research posts at Copenhagen, CERN and Harvard. During this time, his research focus shifted to particle physics and he investigated the nature of relativistic field theories with spontaneously broken symmetries. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Breaking
In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations (or "noise"), the choice will appear arbitrary. This process is called symmetry "breaking", because such transitions usually bring the system from a symmetric but disorderly state into one or more definite states. The phenomenon is part of most theories of everything. Symmetry breaking is thought to play a major role in pattern formation. In his 1972 ''Science'' paper titled "More is different" Nobel laureate P.W. Anderson used the idea of symmetry breaking to show that even if reductionism is true, its converse, constructionism, which is the idea that scientists can easily predict complex phenomena given theories describing their components, is not. Symmetry breaking can be distinguished into two types, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Invariance
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 groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the '' symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called '' gauge bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum
In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing nature. E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen. History The first formulation of a quantum theory describing radiation and matter interaction is attributed to British scientist Paul Dirac, who ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel. The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. Definition An abelian group is a set A, together with an operation \cdot that combines any two elements a and b of A to form another element of A, denoted a \cdot b. The symbo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review
''Physical Review'' is a peer-reviewed scientific journal established in 1893 by Edward Nichols. It publishes original research as well as scientific and literature reviews on all aspects of physics. It is published by the American Physical Society (APS). The journal is in its third series, and is split in several sub-journals each covering a particular field of physics. It has a sister journal, ''Physical Review Letters'', which publishes shorter articles of broader interest. History ''Physical Review'' commenced publication in July 1893, organized by Cornell University professor Edward Nichols and helped by the new president of Cornell, J. Gould Schurman. The journal was managed and edited at Cornell in upstate New York from 1893 to 1913 by Nichols, Ernest Merritt, and Frederick Bedell. The 33 volumes published during this time constitute ''Physical Review Series I''. The American Physical Society (APS), founded in 1899, took over its publication in 1913 and star ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brookhaven National Laboratory
Brookhaven National Laboratory (BNL) is a United States Department of Energy national laboratory located in Upton, Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base and Japanese internment camp. Its name stems from its location within the Town of Brookhaven, approximately 60 miles east of New York City. It is managed by Stony Brook University and Battelle Memorial Institute. Research at BNL includes nuclear and high energy physics, energy science and technology, environmental and bioscience, nanoscience, and national security. The 5,300 acre campus contains several large research facilities, including the Relativistic Heavy Ion Collider and National Synchrotron Light Source II. Seven Nobel Prizes have been awarded for work conducted at Brookhaven Lab. Overview BNL is staffed by approximately 2,750 scientists, engineers, technicians, and support personnel, and hosts 4,000 guest investigators every year. The laboratory has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Mills (physicist)
Robert Laurence Mills (April 15, 1927 – October 27, 1999) was an American physicist, specializing in quantum field theory, the theory of alloys, and many-body theory. While sharing an office at Brookhaven National Laboratory, Chen-Ning Yang and Robert Mills formulated in 1954 a theory now known as the Yang–Mills theory – "the foundation for current understanding of how subatomic particles interact, a contribution which has restructured modern physics and mathematics." Mathematically, Yang and Mills proposed a tensor equation for what are now called Yang–Mills fields (this equation reduces to Maxwell's equations as a special case; see gauge theory): : \partial_F^ + 2 \epsilon ( b_\mu \times F^ ) = J^\nu. Biography Mills was born in Englewood, New Jersey, son of Dorothy C. and Frederick C. Mills. He graduated from George School in Pennsylvania in early 1944. He studied at Columbia College from 1944 to 1948, while on leave from the Coast Guard. Mills demonstrat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chen Ning Yang
Yang Chen-Ning or Chen-Ning Yang (; born 1 October 1922), also known as C. N. Yang or by the English name Frank Yang, is a Chinese theoretical physicist who made significant contributions to statistical mechanics, integrable systems, gauge theory, and both particle physics and condensed matter physics. He and Tsung-Dao Lee received the 1957 Nobel Prize in Physics for their work on parity non-conservation of weak interaction. The two proposed that one of the basic quantum-mechanics laws, the conservation of parity, is violated in the so-called weak nuclear reactions, those nuclear processes that result in the emission of beta or alpha particles. Yang is also well known for his collaboration with Robert Mills in developing non-abelian gauge theory, widely known as the Yang–Mills theory. Biography Yang was born in Hefei, Anhui, China; his father, (; 1896–1973), was a mathematician, and his mother, Meng Hwa Loh Yang (), was a housewife. Yang attended elementary school and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
