Quantum field theory on noncommutative spaces
type: Item
instance of: scholarly article
title: Quantum field theory on noncommutative spaces
zbMATH Open document ID: 1042.81581
DOI: 10.1016/S0370-1573(03)00059-0
author: Richard J. Szabo
published in: Physics Reports
publication date: 2003-04-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0109162
review text: 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.
Mathematics Subject Classification ID: 81T75
zbMATH DE Number: 1895199
zbMATH Keywords: Weyl-Wigner correspondence
zbMATH Keywords: Feynman diagrams
zbMATH Keywords: UV/IR mixing
MaRDI profile type: Publication
arXiv ID: hep-th/0109162
cites work: On Quantized Space-Time
cites work: Compact matrix pseudogroups
cites work: Q3771069
cites work: Constraints on unified gauge theories from noncommutative geometry
cites work: The spectral action principle
cites work: Classical bosons in a non-commutative geometry
cites work: Q4325475
cites work: Duality symmetries and noncommutative geometry of string spacetimes
cites work: String geometry and the noncommutative torus
cites work: Q4251396
cites work: Dirichlet Branes and Ramond-Ramond Charges
cites work: Bound states of strings and \(p\)-branes
cites work: A large-\(N\) reduced model as superstring
cites work: D-branes and short distances in string theory
cites work: Noncommutative geometry and matrix theory: Compactification on tori
cites work: Why Is the Matrix Model Correct?
cites work: Lectures on superstring and M theory dualities
cites work: Non-commutative open string and D-brane
cites work: D-branes and deformation quantization
cites work: String theory and noncommutative geometry
cites work: World volume noncommutativity versus target space noncommutativity
cites work: Instantons on noncommutative \(\mathbb{R}^4\), and \((2,0)\) superconformal six dimensional theory
cites work: Dynamics of strings in noncommutative gauge theory
cites work: Q5569399
cites work: Noncommutative Yang-Mills in IIB matrix model
cites work: Physical instances of noncommuting coordinates
cites work: Noncommutative Dirac-Born-Infeld action for D-brane.
cites work: The non-abelian Born-Infeld action and noncommutative gauge theory
cites work: Q4421399
cites work: REVIEW OF THE PHENOMENOLOGY OF NONCOMMUTATIVE GEOMETRY
cites work: Construction of non-Abelian gauge theories on noncommutative spaces
cites work: Deformation quantization for actions of 𝑅^{𝑑}
cites work: Q5340842
cites work: Q4693938
cites work: Q5788173
cites work: Deformation theory and quantization. I: Deformations of symplectic structures
cites work: Deformation quantization of Poisson manifolds
cites work: A path integral approach to the Kontsevich quantization formula.
cites work: Non-commutative solitons
cites work: D-branes and strings as noncommutative solitons
cites work: Noncommutative perturbative dynamics
cites work: Quantum field theory techniques in graphical enumeration
cites work: Wilson loops in noncommutative Yang-Mills
cites work: Divergencies in a field theory on quantum space.
cites work: Quantum field theory on noncommutative space-times and the persistence of ultraviolet divergences
cites work: A consistent noncommutative field theory: the Wess-Zumino model.
cites work: Wess-Zumino-Witten and fermion models in noncommutative space
cites work: Open strings in a B-field background as electric dipoles.
cites work: Comments on noncommutative perturbative dynamics
cites work: On the stringy nature of winding modes in non-commutative thermal field theories
cites work: Non-commutative gauge dynamics from the string worldsheet
cites work: THE NONCOMMUTATIVE SUPERSYMMETRIC NONLINEAR SIGMA MODEL
cites work: Ultraviolet properties of noncommutative nonlinear \(\sigma\)-models in two dimensions
cites work: Superfield effective action in the noncommutative Wess-Zumino model
cites work: Space/time non-commutativity and causality
cites work: Lorentz transformation and light-like noncommutative SYM
cites work: \(S\)-duality and noncommutative gauge theory
cites work: Noncommutative gauge dynamics from brane configurations with background \(B\) field
cites work: On theories with light-like noncommutativity
cites work: Restrictions on gauge groups in noncommutative gauge theory
cites work: Comments on perturbative dynamics of non-commutative Yang-Mills theory
cites work: A path integral representation of the map between commutative and noncommutative gauge fields
cites work: On open string \(\sigma\)-model and noncommutative gauge fields.

Quantum field theory on noncommutative spaces (cites work)
cites work: Finite \(N\) Matrix models of noncommutative gauge theory

Quantum field theory on noncommutative spaces (cites work)
cites work: Lattice gauge fields and discrete non-commutative Yang-Mills theory

Quantum field theory on noncommutative spaces (cites work)
cites work: Wilson lines on noncommutative tori

Quantum field theory on noncommutative spaces (cites work)
cites work: Observables of non-commutative gauge theories

Quantum field theory on noncommutative spaces (cites work)
cites work: A note on gauge invariant operators in noncommutative gauge theories and the Matrix model

Quantum field theory on noncommutative spaces (cites work)
cites work: PERTURBATIVE QUANTUM GAUGE FIELDS ON THE NONCOMMUTATIVE TORUS

Quantum field theory on noncommutative spaces (cites work)
cites work: The IR/UV connection in non-commutative gauge theories

Quantum field theory on noncommutative spaces (cites work)
cites work: One-Loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative ℝ 4 </mml:m

Quantum field theory on noncommutative spaces (cites work)
cites work: One loop renormalizability of supersymmetric Yang-Mills theories on noncommutative two-torus

Quantum field theory on noncommutative spaces (cites work)
cites work: Perturbative analysis on infrared aspects of noncommutative QED on \(\mathbb R^ 4\).

Quantum field theory on noncommutative spaces (cites work)
cites work: UV/IR mixing via closed strings and tachyonic instabilities

Quantum field theory on noncommutative spaces (cites work)
cites work: Dynamical breaking of supersymmetry in noncommutative gauge theories

Quantum field theory on noncommutative spaces (cites work)
cites work: Renormalization of non-commutative U\((N)\) gauge theories

Quantum field theory on noncommutative spaces (cites work)
cites work: Bounding noncommutative QCD

Quantum field theory on noncommutative spaces (cites work)
cites work: BPS states on non-commutative tori and duality

Quantum field theory on noncommutative spaces (cites work)
cites work: Q4270934

Quantum field theory on noncommutative spaces (cites work)
cites work: Some twisted self-dual solutions for the Yang-Mills equations on a hypertorus

Quantum field theory on noncommutative spaces (cites work)
cites work: Branes, fluxes and duality in M(atrix)-theory

Quantum field theory on noncommutative spaces (cites work)
cites work: Morita equivalence and \(T\)-duality (or \(B\) versus \(\Theta\)).

Quantum field theory on noncommutative spaces (cites work)
cites work: Morita equivalence and duality.

Quantum field theory on noncommutative spaces (cites work)
cites work: Q5664012

Quantum field theory on noncommutative spaces (cites work)
cites work: MORITA EQUIVALENCE OF MULTIDIMENSIONAL NONCOMMUTATIVE TORI

Quantum field theory on noncommutative spaces (cites work)
cites work: Matrix theory compactification on noncommutative \(\mathbb T^4/\mathbb{Z}_2\)

Quantum field theory on noncommutative spaces (cites work)
cites work: Projective Modules over Higher-Dimensional Non-Commutative Tori

Quantum field theory on noncommutative spaces (cites work)
cites work: Infinite-dimensional algebras, sine brackets, and SU(\(\infty)\)

Quantum field theory on noncommutative spaces (cites work)
cites work: Supermatrix models

Quantum field theory on noncommutative spaces (cites work)
cites work: String scale in noncommutative Yang-Mills

Quantum field theory on noncommutative spaces (cites work)
cites work: Noncommutative geometry and spacetime gauge symmetries of string theory

Quantum field theory on noncommutative spaces (cites work)
cites work: Supercurrent interactions in noncommutative Yang-Mills and IIB matrix model

Quantum field theory on noncommutative spaces (cites work)
cites work: Deformation quantization of Hermitian vector bundles

Quantum field theory on noncommutative spaces (cites work)
cites work: On the uniqueness of the Heisenberg commutation relations

Quantum field theory on noncommutative spaces (cites work)
cites work: Gravity coupled with matter and the foundation of non-commutative geometry

Quantum field theory on noncommutative spaces (cites work)
cites work: The homotopy type of the unitary group of Hilbert space

Quantum field theory on noncommutative spaces (cites work)
cites work: Q4820365

Quantum field theory on noncommutative spaces (cites work)
cites work: Comments on noncommutative gauge theories

Quantum field theory on noncommutative spaces (cites work)
cites work: Noncommutative instantons: A new approach

Quantum field theory on noncommutative spaces (cites work)
cites work: Q3704051

Quantum field theory on noncommutative spaces (cites work)
cites work: On the homotopy type of certain groups of operators

Quantum field theory on noncommutative spaces (cites work)
cites work: Exact noncommutative solitons

Quantum field theory on noncommutative spaces (cites work)
cites work: From large \(N\) matrices to the noncommutative torus

Quantum field theory on noncommutative spaces (OpenAlex ID)
OpenAlex ID: W2161879643

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: Quantum field theory on noncommutative spaces
Similarity Score: 1.0
Recommender Run: Recommender Run 3

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: Q3065228
Similarity Score: 0.97049564
Recommender Run: Recommender Run 3

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: Noncommutative quantum field theory
Similarity Score: 0.97049564
Recommender Run: Recommender Run 3

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: Quantum fields on noncommutative spacetimes: theory and phenomenology
Similarity Score: 0.9656477
Recommender Run: Recommender Run 3

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: Quantum Fields and Noncommutative Spacetime
Similarity Score: 0.96507376
Recommender Run: Recommender Run 3

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: Noncommutative field theory from quantum mechanical space-space noncommutativity
Similarity Score: 0.9645618
Recommender Run: Recommender Run 3

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: NONCOMMUTATIVE QUANTIZATION FOR NONCOMMUTATIVE FIELD THEORY
Similarity Score: 0.964449
Recommender Run: Recommender Run 3

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: Q3509527
Similarity Score: 0.964449
Recommender Run: Recommender Run 3

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: Noncommutative and non-anticommutative quantum field theory
Similarity Score: 0.9621342
Recommender Run: Recommender Run 3

Quantum field theory on noncommutative spaces (Recommended article)
Recommended article: Noncommutative field theory
Similarity Score: 0.95691425
Recommender Run: Recommender Run 3