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C-theorem
In quantum field theory the ''C''-theorem states that there exists a positive real function, C(g^_i,\mu), depending on the coupling constants of the quantum field theory considered, g^_i, and on the energy scale, \mu^_, which has the following properties: *C(g^_i,\mu) decreases monotonically under the renormalization group (RG) flow. *At fixed points of the RG flow, which are specified by a set of fixed-point couplings g^*_i, the function C(g^*_i,\mu)=C_* is a constant, independent of energy scale. The theorem formalizes the notion that theories at high energies have more degrees of freedom than theories at low energies and that information is lost as we flow from the former to the latter. Two-dimensional case Alexander Zamolodchikov proved in 1986 that two-dimensional quantum field theory always has such a ''C''-function. Moreover, at fixed points of the RG flow, which correspond to conformal field theories, Zamolodchikov's ''C''-function is equal to the central charge of the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugh Osborn
Hugh Osborn is a British theoretical high-energy physicist and a professor emeritus at the University of Cambridge, Department of Applied Mathematics and Theoretical Physics. He is known for his work on Conformal Field Theory and Quantum Field Theory. Education Osborn obtained his PhD in 1967 from the University College London. His PhD advisor was Sigurd Zienau. Career and research After postdoctoral research positions at the University of Sussex and Queen Mary University of London, he became a professor first at the University of Glasgow and then in 1971 moved to the University of Cambridge where he remained ever since. He is a fellow of Trinity College. In April 2020 he was elected a Fellow of the Royal Society. In 1989, Osborn obtained the first proof of the four-dimensional C-theorem, which was conjectured one year earlier by John Cardy. Osborn's proof was applicable to renormalization group flows which are perturbative, that is do not deviate far from the free quantum f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Zamolodchikov
Alexander Borisovich Zamolodchikov (russian: Алекса́ндр Бори́сович Замоло́дчиков; born September 18, 1952) is a Russian physicist, known for his contributions to condensed matter physics, two-dimensional conformal field theory, and string theory, and is currently the C.N. Yang/Wei Deng Endowed Chair of Physics at Stony Brook University. Biography Born in Novo-Ivankovo, now part of Dubna, Zamolodchikov earned a M.Sc. in Nuclear Engineering (1975) from Moscow Institute of Physics and Technology, a Ph.D. in Physics from the Institute for Theoretical and Experimental Physics (1978). He joined the research staff of Landau Institute for Theoretical Physics (1978) where he got an honorary doctorate (1983). He co-authored the famous BPZ paper "Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory", with Alexander Polyakov and Alexander Belavin. He joined Rutgers University (1990) where he co-founded Rutgers New High Energy Theory Center ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renormalization Group
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle. A change in scale is called a scale transformation. The renormalization group is intimately related to ''scale invariance'' and ''conformal invariance'', symmetries in which a system appears the same at all scales (so-called self-similarity). As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller sca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RG Flow
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle. A change in scale is called a scale transformation. The renormalization group is intimately related to ''scale invariance'' and ''conformal invariance'', symmetries in which a system appears the same at all scales (so-called self-similarity). As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller sca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zohar Komargodski
Zohar Komargodski (born 10 March 1983) is an Israeli theoretical physicist who works on quantum field theory, including conformal field theories, gauge theories and supersymmetry. Komargodski received his Ph.D. from the Weizmann Institute in 2008 and worked as a postdoctoral researcher at the Institute for Advanced Study in Princeton afterwards. He currently holds a professor position at the Simons Center for Geometry and Physics at Stony Brook University in New York. Research In 2011 he and Adam Schwimmer from the Weizmann Institute proved a long-standing conjecture in quantum field theory, the a-theorem, conjectured in 1988 by John Cardy. Cardy's conjecture was a generalization of the c-theorem by Alexander Zamolodchikov (1986) for two-dimensional quantum field theories on higher dimensions. The c-theorem ensures the existence of a function that decreases monotonically with the flow of the renormalization group (RG) (a function of the coupling constants and energy scale), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Field Theory
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points. Scale invariance vs conformal invariance In quantum field theory, scale invariance is a common and natural symmetry, because any fixed point of the renormalization group is by definition scale invariant. Conformal symmetry is stronger than scale invariance, and one needs additional assumptions to argue that it should appear in nature. The basic idea behind its plausibility is that ''local'' scale invariant theories have their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renormalization Group
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle. A change in scale is called a scale transformation. The renormalization group is intimately related to ''scale invariance'' and ''conformal invariance'', symmetries in which a system appears the same at all scales (so-called self-similarity). As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller sca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
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 and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coupling Constant
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, r^2, between the bodies; thus: G in F=G m_1 m_2/r^2 for Newtonian gravity and k_\text in F=k_\textq_1 q_2/r^2 for electrostatic. This description remains valid in modern physics for linear theories with static bodies and massless force carriers. A modern and more general definition uses the Lagrangian \mathcal (or equivalently the Hamiltonian \mathcal) of a system. Usually, \mathcal (or \mathcal) of a system describing an interaction can be separated into a ''kinetic part'' T and an ''interaction part'' V: \mathcal=T-V (or \mathcal=T+V). In field theory, V always contains 3 fields te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-dimensional Conformal Field Theory
A two-dimensional conformal field theory is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations. In contrast to other types of conformal field theories, two-dimensional conformal field theories have infinite-dimensional symmetry algebras. In some cases, this allows them to be solved exactly, using the conformal bootstrap method. Notable two-dimensional conformal field theories include minimal models, Liouville theory, massless free bosonic theories, Wess–Zumino–Witten models, and certain sigma models. Basic structures Geometry Two-dimensional conformal field theories (CFTs) are defined on Riemann surfaces, where local conformal maps are holomorphic functions. While a CFT might conceivably exist only on a given Riemann surface, its existence on any surface other than the sphere implies its existence on all surfaces. Given a CFT, it is indeed possible to glue two Riemann surfaces where it exists, and obtain t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Charge
In theoretical physics, a central charge is an operator ''Z'' that commutes with all the other symmetry operators. The adjective "central" refers to the center of the symmetry group—the subgroup of elements that commute with all other elements of the original group—often embedded within a Lie algebra. In some cases, such as two-dimensional conformal field theory, a central charge may also commute with all of the other operators, including operators that are not symmetry generators. Overview More precisely, the central charge is the charge that corresponds, by Noether's theorem, to the center of the central extension of the symmetry group. In theories with supersymmetry, this definition can be generalized to include supergroups and Lie superalgebras. A central charge is any operator which commutes with all the other supersymmetry generators. Theories with extended supersymmetry typically have many operators of this kind. In string theory, in the first quantized formali ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Cardy
John Lawrence Cardy FRS (born 19 March 1947, England)Guggenheim Foundation: Annual Report 1985. is a British-American theoretical physicist at the University of California, Berkeley. He is best known for his work in theoretical condensed matter physics and statistical mechanics, and in particular for research on critical phenomena and two-dimensional conformal field theory. He was an undergraduate and postgraduate student at Downing College, University of Cambridge, before moving to the University of California, Santa Barbara, where he joined the faculty in 1977. In 1993, he moved to the University of Oxford, where until 2014 he was a Fellow of All Souls College (now Emeritus) and a Professor of Physics in the Rudolf Peierls Centre for Theoretical Physics. He currently holds a Visiting Professorship at the University of California, Berkeley. He was elected as a Fellow of the Royal Society in 1991, received the Dirac Medal of the IoP in 2000, was awarded the Lars Onsager Prize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
