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Infinite dimensional Lie algebra occurring in quantum field theory
relations among the current density operators in quantum field theories define an infinite-dimensional Lie algebra called a current algebra. Mathematically
Current_algebra
Creating a "larger" Lie algebra from a smaller one, in one of several ways
algebra which is isomorphic with an untwisted affine Kac–Moody algebra. Using the centrally extended loop algebra one may construct a current algebra
Lie_algebra_extension
Lowest energy state in quantum chromodynamics
realization is also known as Witten–Veneziano mechanism. PCAC and current algebra also provide evidence for this pattern of SSB. Direct estimates of
QCD_vacuum
Construction in algebra
In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra and a (counital coassociative)
Hopf_algebra
American theoretical physicist (1929–2019)
elementary particles and their interactions. In the 1960s, he introduced current algebra as a method of systematically exploiting symmetries to extract predictions
Murray_Gell-Mann
Type of 2D conformal field theory
group (or supergroup), and its symmetry algebra is the affine Lie algebra built from the corresponding Lie algebra (or Lie superalgebra). By extension, the
Wess–Zumino–Witten_model
Topological complex vector space
mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties
C*-algebra
Method to convey chess moves
Algebraic notation is the standard method of chess notation, used for recording and describing moves. It is based on a system of coordinates to uniquely
Algebraic_notation_(chess)
Non-conservation of chiral current in physics
to the anomalous decay rate of the neutral pion, as computed in the current algebra of the chiral model. These calculations suggested that the decay of
Chiral_anomaly
Algebra used in 2D conformal field theories and string theory
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string
Vertex_operator_algebra
Branch of mathematics
study include algebraic equations, algebraic varieties, and schemes. Current methods in computational nonlinear algebra can be broadly broken into two domains:
Nonlinear_algebra
Pakistani theoretical physicist (1930–2013)
carried out research in the field of current algebra, where they applied the mathematical framework of current algebra in the applications of radiative decays
Riazuddin_(physicist)
Algebraic structure designed for geometry
geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is
Geometric_algebra
Type of Kac–Moody algebras
affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. Given
Affine_Lie_algebra
Supersymmetric extension to the Virasoro algebra
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There
Super_Virasoro_algebra
American theoretical physicist
Jackiw, David Gross, Sam B. Treiman, Edward Witten, Bruno Zumino. Current Algebra and Anomalies: A Set of Lecture Notes and Papers. World Scientific
Edward_Witten
Setting of relativistic physics in geometric algebra
spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) of physics. Spacetime algebra provides
Spacetime_algebra
Relation between static and dynamic quantities
with the optical theorem, using the operator product expansion or current algebra. Quantum field theory sum rules are useful in a variety of ways. They
Sum rules (quantum field theory)
Sum_rules_(quantum_field_theory)
Academic journal
Linear Algebra and Its Applications is a biweekly peer-reviewed mathematics journal published by Elsevier and covering matrix theory and finite-dimensional
Linear Algebra and Its Applications
Linear_Algebra_and_Its_Applications
Particle smaller than an atom
Quark". indicate 1947. Fritzsch, Harald; Gell-Mann, Murray (1972). "Current algebra: Quarks and what else?". EConf. C720906V2: 135–165. arXiv:hep-ph/0208010
Subatomic_particle
Concept in mathematics
infinite-dimensional Lie theory appeared for the first time, in the shape of current algebra. Intuitively, a Lie pseudogroup should be a pseudogroup which "originates"
Pseudogroup
Phenomenon in particle physics
heavy-heavy-strange baryons. Conformal anomaly Little Higgs Top Quark Condensate See Current algebra. Chiral symmetry breaking in QCD is furthermore intimately associated
Chiral_symmetry_breaking
1966 mathematics textbook by Serge Lang
Linear Algebra is a 1966 mathematics textbook by Serge Lang. The third edition of 1987 covers fundamental concepts of vector spaces, matrices, linear
Linear_Algebra_(book)
Pakistani emeritus professor of theoretical physics (born 1930)
bag model. Riazuddin, A.Q.; Sarker, Fayyazuddin (1 August 1968). "Current algebra, spectral function sum rules and the f − (0) / ƒ+(0) ratio in Kℓ3 decay"
Fayyazuddin
Kac–Moody algebra. KZ Initials of Knizhnik and Zamolodchikov, as in KZ equation, a differential equation related to the primary fields of a current algebra. L
Glossary_of_string_theory
Basic concepts of algebra
{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted
Elementary_algebra
American physicist (born 1939)
work concerns the invention of effective Lagrangian method, the first current algebra analysis of pion-pion scattering and solution to the notorious U(1)
Pran_Nath_(physicist)
Quantum field theory
Princeton University Press. ISBN 0691029784. Cao, Tian Yu (2010). From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism (1st ed.)
Yang–Mills_theory
Mathematical group of loops in a Lie group
to affine Kac–Moody algebras, conformal field theory, and the Verlinde formula. In algebraic geometry one also studies algebraic loop groups, defined
Loop_group
Partial differential equations of correlation functions
two-dimensional conformal field theories associated with an affine Lie algebra at a fixed level. They form a system of complex partial differential equations
Knizhnik–Zamolodchikov equations
Knizhnik–Zamolodchikov_equations
Academic journal
Communications in Algebra is a monthly peer-reviewed scientific journal covering algebra, including commutative algebra, ring theory, module theory, non-associative
Communications_in_Algebra
Academic journal
Index Expanded Current Contents/Physical Chemical and Earth Sciences Journal Citation Reports/Science Edition INSPEC "Journal of Algebra and its Applications"
Journal of Algebra and Its Applications
Journal_of_Algebra_and_Its_Applications
American physicist
J. D. (1966-08-26). "Applications of the Chiral U ( 6 ) ⊗ U ( 6 ) Algebra of Current Densities". Physical Review. 148 (4): 1467–1478. Bibcode:1966PhRv
Kenneth_Alan_Johnson
American physicist
neutrino processes, current algebra, soft pion theorems, sum rules, and perturbation theory anomalies helped lay the foundations for the current Standard Model
Stephen_L._Adler
Quantum mechanical equation of motion of charged particles in magnetic field
Fröhlich, Jürg; Studer, Urban M. (1993-07-01). "Gauge invariance and current algebra in nonrelativistic many-body theory". Reviews of Modern Physics. 65
Pauli_equation
Isosinglet meson made of quarks and antiquarks
Bibcode:1976PhRvL..37....8T. doi:10.1103/PhysRevLett.37.8. Witten, E. (1979). "Current algebra theorems for the U(1) "Goldstone boson"". Nuclear Physics B. 156 (2):
Eta_and_eta_prime_mesons
Academic journal
Electronic Journal of Linear Algebra is a peer-reviewed platinum open access scientific journal covering matrix analysis and linear algebra, together with their
Electronic Journal of Linear Algebra
Electronic_Journal_of_Linear_Algebra
Academic journal of mathematical research
establishment in 2009. It is currently published four times per year. Historically, the Journal of Commutative Algebra filled a niche for the Rocky Mountain
Journal of Commutative Algebra
Journal_of_Commutative_Algebra
Breakdown of gauge symmetry at the quantum level
Green–Schwarz mechanism Mixed anomaly Treiman, Sam, and Roman Jackiw, (2014). Current algebra and anomalies. Princeton University Press. Cheng, T.P.; Li, L.F. (1984)
Gauge_anomaly
English physicist (born 1943)
birthday in 2003. His DPhil thesis analyzed the relationship between current algebra and superconvergence sum rules, and contained a 1967 sum rule. In 1970
Paul_Frampton
Indian particle physicist (1942-2026)
applications of algebra in the discipline and his thesis was subsequently published by the university under the title, Current-algebra Applications in
Probir_Roy
Academic journal
The International Journal of Algebra and Computation is published by World Scientific, and contains articles on general mathematics, as well as: Combinatorial
International Journal of Algebra and Computation
International_Journal_of_Algebra_and_Computation
Japanese theoretical physicist
Corrections toβDecay and the Quantum Numbers of Fields Underlying Current Algebra". Physical Review Letters. 18 (26): 1224–1225. Bibcode:1967PhRvL..18
Hiroshi_Suura
Formal systems of logic that significantly differ from standard logical systems
abstract algebraic logic has also provided means to classify logics, with most results having been obtained for propositional logics. The current algebraic hierarchy
Non-classical_logic
In mathematics, a Nakayama algebra or generalized uniserial algebra is an algebra such that each left or right indecomposable projective module has a unique
Nakayama_algebra
Academic journal
Applied Algebra is a monthly peer-reviewed scientific journal covering that part of algebra likely to be of general mathematical interest: algebraic results
Journal of Pure and Applied Algebra
Journal_of_Pure_and_Applied_Algebra
CPMP-Tools is a free open-source software-package for Computer Algebra System (CAS). CPMP is an abbreviation for Core-Plus Mathematics Project. CPMP-Tools
CPMP-Tools
%5B%5BWikipedia%3ARedirects+for+discussion%5D%5D+debate+closed+as+delete #REDIRECT Group algebra of a locally compact group From a subtopic: This is a redirect from a subtopic
Stereotype_group_algebra
American theoretical physicist (1936–2013)
doi:10.1103/RevModPhys.47.773. Wilson, K. G. Non-lagrangian models in current algebra Physical Review, 179, 1969, p. 1499–1512; Model of coupling constant
Kenneth_G._Wilson
Property of particles related to spin
that actually treats them differently, known as axial symmetry. (cf. Current algebra.) A scalar field model encoding chiral symmetry and its breaking is
Chirality_(physics)
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Field of knowledge
including number theory (the study of integers and their properties), algebra (the study of operations and the structures they form), geometry (the study
Mathematics
Yang–Mills theory vacuum state
ISBN 978-0-521-67054-8. Witten, E.; Jackiw, R.; Treiman, S.; Zumino, B. (1985). Current Algebra And Anomalies. World Scientific Publishing. pp. 298–300. Bibcode:1985caa
Theta_vacuum
Field of mathematics using techniques from combinatorics and commutative algebra
Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of
Combinatorial commutative algebra
Combinatorial_commutative_algebra
Element of interest in an algebraic structure
topological algebra: S is a generating set of a topological algebra A if the smallest closed subalgebra of A containing S is A Generating a σ-algebra by a collection
Generator_(mathematics)
current-status-of-grothendiecks-homotopy-hypothesis-and-whiteheads-algebraic-h https://ncatlab.org/nlab/show/algebraic+homotopy Handbook of Algebraic
Algebraic_homotopy
Conformal field theory on a spacetime with a boundary
Operator product expansion Critical point Affleck, Ian (1990). "A current algebra approach to the Kondo effect". Nuclear Physics B. 336 (3). Elsevier
Boundary conformal field theory
Boundary_conformal_field_theory
symmetry considerations, and introduced non-abelian Lie groups to current algebra and so the gauge theories that came to supersede it. The 1960s and
History of quantum field theory
History_of_quantum_field_theory
Academic journal
the goal of "providing an alternative to the current range of commercial specialty journals in algebra and number theory, an alternative of higher quality
Algebra_&_Number_Theory
Symmetry between bosons and fermions
algebra requires the introduction of a Z2-grading under which the bosons are the even elements and the fermions are the odd elements. Such an algebra
Supersymmetry
American theoretical physicist
breaking of a continuous symmetry." He also worked on the application of "current algebra" to the geometry of macroscopic quantum flows in superfluid helium
Harry_Lee_Morrison
British physicist
Media. 7 October 2014. p. 37. Wallace, David (1971). Applications of Current Algebras and Chiral Symmetry Breaking. ed.ac.uk (PhD thesis). University of
David_Wallace_(physicist)
American theoretical physicist (1941–2025)
symmetry. W. A. Bardeen, H. Fritzsch, and M. Gell-Mann, "Light cone current algebra, π 0 {\displaystyle \pi ^{0}} decay, and e + e − {\displaystyle e^{+}e^{-}}
William_A._Bardeen
Notable events in the history of algebra
a timeline of key developments of algebra: Mathematics portal History of algebra – Historical development of algebra Archibald, Raymond Clare (December
Timeline_of_algebra
Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical
Numerical_algebraic_geometry
Argentine theoretical physicist (1930–2022)
Reports, Vol. 88, 1982, pp. 1–90 doi:10.1016/0370-1573(82)90100-4 Current algebra formulation of radiation corrections in gauge theories and the universality
Alberto_Sirlin
Type of topological solutions in non-linear sigma models
Namik K.; Tze, Hsiung Chia (January 1, 1979). "Chiral solitons and current algebra". Annals of Physics. 117 (1): 164–194. doi:10.1016/0003-4916(79)90048-4
Skyrmion
Method in computational algebra
the Cantor–Zassenhaus algorithm of 1981. It is currently implemented in many well-known computer algebra systems. Berlekamp's algorithm takes as input
Berlekamp's_algorithm
Classification scheme of hadrons
B1006. Bardeen, W.; Fritzsch, H.; Gell-Mann, M. (1973). "Light cone current algebra, π0 decay, and e+ e− annihilation". In Gatto, R. (ed.). Scale and conformal
Quark_model
S2CID 6172445. Faddeev, L. D.; Volkov, A. Yu. (1993). "Abelian current algebra and the Virasoro algebra on the lattice". Physics Letters B. 315 (3–4): 311–318
Quantum_dilogarithm
Physical mechanism creating dimensionful parameters
setting up a mass scale. See conformal anomaly. Cao, Tian Yu. From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism. Cambridge
Dimensional_transmutation
Russian university
precision medicine". Medcity News. Knizhnik VG, Zamolodchikov AB (1984). "Current algebra and Wess-Zumino model in two dimensions". Nucl. Phys. B. 247 (1): 83–103
Moscow Institute of Physics and Technology
Moscow_Institute_of_Physics_and_Technology
Number
rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently
0
Associative algebra generalizing the Virasoro algebra
theory and representation theory, a W-algebra is an associative algebra that generalizes the Virasoro algebra. W-algebras were introduced by Alexander Zamolodchikov
W-algebra
Array of numbers
"two-by-three matrix", a 2 × 3 matrix, or a matrix of dimension 2 × 3. In linear algebra, matrices are used as linear maps. In geometry, matrices are used for geometric
Matrix_(mathematics)
Series of mathematics books by Nicolas Bourbaki
treated in the series include set theory, abstract algebra, topology, analysis, Lie groups and Lie algebras. The unusual singular "mathématique" (mathematic)
Éléments_de_mathématique
American physicist (1934–2024)
Quantum Fields. McGraw-Hill. ISBN 0-07-005494-0. J. D. Bjorken (1968). "Current Algebra at Small Distances", in Proceedings of the International School of
James_Bjorken
%5B%5BWikipedia%3ARedirects+for+discussion%5D%5D+debate+closed+as+delete #REDIRECT Group algebra of a locally compact group
Stereotypical_group_algebra
Generalization of a Lie algebra
A Lie conformal algebra is in some sense a generalization of a Lie algebra in that it too is a "Lie algebra," though in a different pseudo-tensor category
Lie_conformal_algebra
2D supersymmetric generalization to the conformal algebra
In mathematical physics, the 2D N = 2 superconformal algebra is an infinite-dimensional Lie superalgebra, related to supersymmetry, that occurs in string
N_=_2_superconformal_algebra
Family of approaches for modelling concurrent systems
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process
Process_calculus
Riemannian manifold with SU(n) holonomy
In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has certain properties
Calabi–Yau_manifold
Area of mathematics
algorithm design, computational complexity, numerical methods and computer algebra. Computational mathematics refers also to the use of computers for mathematics
Computational_mathematics
British quantum physicist (1935–2025)
and for his work on algebraic descriptions of quantum mechanics in terms of underlying symplectic and orthogonal Clifford algebras. Hiley co-authored the
Basil_Hiley
theoretical physics from Princeton University. His dissertation was titled: “Current Algebras as Unitary Representations of Groups.” During this time, he also studied
Gerald_Goldin
Equations describing classical electromagnetism
that every closed 2-form is exact. Other formalisms include the geometric algebra formulation and a matrix representation of Maxwell's equations. Historically
Maxwell's_equations
Academic journal
Grätzer, is currently published by Springer-Verlag. Honorary editors in chief of the journal included Alfred Tarski and Bjarni Jónsson. Algebra Universalis
Algebra_Universalis
Open-source software
OpenBLAS is an open-source implementation of the BLAS (Basic Linear Algebra Subprograms) and LAPACK APIs with many hand-crafted optimizations for specific
OpenBLAS
Lie group of Lorentz transformations
group on Minkowski space uses biquaternions, which form a composition algebra. The isometry property of Lorentz transformations holds according to the
Lorentz_group
Quantity used to describe the mathematical state of a dynamical system
using self-adjoint elements from a Cstar_algebra, then a state is a normalized positive element of the algebra's dual (a continuous linear functional ρ):
State_variable
director, writer, and producer. Michael Hopkins New 1979 United States Algebraic topology expert Ruth Karras Yale University New 1979 United States Historian
List_of_Rhodes_Scholars
Mathematical object that describes the electromagnetic field in spacetime
ρ , J ) {\displaystyle J^{\alpha }=(c\rho ,\mathbf {J} )} is the four-current. In magnetostatics and magnetodynamics, Gauss's law for magnetism and Maxwell–Faraday
Electromagnetic_tensor
REDUCE is a general-purpose computer algebra system originally geared towards applications in physics. The development of REDUCE was started in 1963 by
Reduce (computer algebra system)
Reduce_(computer_algebra_system)
Representation theory of the symmetries of manifolds
interest in the topic to research in theoretical physics of the local current algebra, in the preceding years. Research on the finite configuration representations
Representation theory of diffeomorphism groups
Representation_theory_of_diffeomorphism_groups
Canadian-American mathematician
1970) is a Canadian-American mathematician working in algebraic geometry. He is the current president of the American Mathematical Society. Vakil was
Ravi_Vakil
Nonlinear equation which arises on linear optimal control problems
An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time
Algebraic_Riccati_equation
Computer algebra system
commutative algebra and algebraic geometry. Macaulay2 is built around fast implementations of algorithms useful for computation in commutative algebra and algebraic
Macaulay2
Topics referred to by the same term
the applied voltage Receiver operating characteristic Characteristic (algebra) of a ring, the smallest common cycle length of the ring's addition operation
Characteristic
Email service provided by Google
Latin alphabet. The modern AJAX version is officially supported in the current and previous major releases of Google Chrome, Firefox, Microsoft Edge and
Gmail
Harvey White B&W series of films (30m each) 1957 titles (incomplete): Algebra and Powers of Ten / The Atmosphere / Atomic Accelerators / The Bohr Atom
List of Encyclopædia Britannica Films titles
List_of_Encyclopædia_Britannica_Films_titles
CURRENT ALGEBRA
CURRENT ALGEBRA
CURRENT ALGEBRA
CURRENT ALGEBRA
CURRENT ALGEBRA
CURRENT ALGEBRA
CURRENT ALGEBRA
CURRENT ALGEBRA
CURRENT ALGEBRA