Quantum field theory on noncommutative spaces

By R. Szabo. 2001

1,346 citations recorded by the source corpus.

Abstract A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl–Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang–Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang–Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e881fb0d58252bfefbb31198338a3cbcab116c9b

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Citations in the corpus

New realizations of Lie algebra kappa-deformed Euclidean space (2006, background): “In the last decade, there has been a great interest in the formulation and consistency of physical theories defined on noncommutative (NC) spaces, and in finding their consequences [1-5].”
Infinitely many star products to play with (2001, background): “On the technical level, properties of the Moyal multiplier algebra M(R2nθ ) are elucidated.”
Membrane sigma-models and quantization of non-geometric flux backgrounds (2012, methodology): “By using the nonassociative convolution product induced by horizontal multiplication in G , we induce a nonassociative star product on the algebra of functions on phase space by embedding it as an algebra object in the category G , in the spirit of [15]; this mapping can be regarded as a higher vers”
Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory (2015, methodology): “We refer the reader to the extensive reviews [32, 33].”
κ-Minkowski spacetime and the star product realizations (2007, background): “In order to accomodate for quantum aspects of spacetime, spacetime noncommutativity has been studied extensively [1],[2],[3],[4],[5],[6] and two main directions in the investigation have focused on the canonical noncommutative spacetime and κ-Minkowski noncommutative spacetime [7]-[32], respectively”
Spin-half fermions with mass dimension one: theory, phenomenology, and dark matter (2004, background): “Yet attempts to merge the quantum, the relativistic, and the gravitational realms immediately ask for an element of non-locality which may be realized for example in the framework of field theories on non-commutative spaces (for reviews, see for example [22, 23]).”
Quantum-Spacetime Phenomenology (2008, background): “[101]) that is found to be applicable to the description of strings in the presence of a constant Neveu–Schwarz two-form (“Bμν”) field [213, 516].”
Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces (2003, background): “Noncommutative Yang-Mills theory defined on a 2n-dimensional torus is manifestly invariant under the standard SO(2n, 2n,Z) open string T-duality transformations [3] θ̃ = (A θ + B)> (θQ− N)−1 , H̃ = (θQ− N)>H (θQ− N) , g̃(2) YM = g 2 YM det(θQ− N) , (B.”
Symmetry, gravity and noncommutativity (2006, methodology): “ old material indicating that gravitation 3 is naturally contained in the gauge-invariant dynamics of noncommutative Yang-Mills theory on ﬂat space. While some of this material is already reviewed in [114], we revisit the subject with more of an emphasis on the manner in which the constructions are ”