Gauge theories on quantum spaces

Abstract

We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory models on Moyal spaces as well as on quantum spaces whose coordinates form a Lie algebra are covered, with particular emphasis on some explored quantum properties. Recent attempts aiming to include gravity dynamics within a noncommutative framework are also considered.

141 pages. Review article. This is a preliminary version

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Cited by in corpus (13)

• Constructing noncommutative black holes
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• On Poisson Electrodynamics With Charged Fields
• Field theories on $\rho$-deformed Minkowski space-time
• Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Hamiltonian analysis in Lie-Poisson gauge theory
• Light Propagation in $\kappa$-Minkowski Space-Time: Gauge Ambiguities and Invariance
• Non-commutative gauge symmetry from strong homotopy algebras
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories
• Quantum causality in $\kappa$-Minkowski and related constraints
• Star-products for Lie-algebraic noncommutative Minkowski space-times
• Noncommutative dyonic black holes sourced by nonlinear electromagnetic fields