Poisson gauge theory

Abstract

The Poisson gauge algebra is a semi-classical limit of complete non-commutative gauge algebra. In the present work we formulate the Poisson gauge theory which is a dynamical field theoretical model having the Poisson gauge algebra as a corresponding algebra of gauge symmetries. The proposed model is designed to investigate the semi-classical features of the full non-commutative gauge theory with coordinate dependent non-commutativity ${\Theta }^{ab}(x)$, especially whose with a non-constant rank. We derive the expression for the covariant derivative of matter field. The commutator relation for the covariant derivatives defines the Poisson field strength which is covariant under the Poisson gauge transformations and reproduces the standard $U(1)$ field strength in the commutative limit. We derive the corresponding Bianchi identities. The field equations for the gauge and the matter fields are obtained from the gauge invariant action. We consider different examples of linear in coordinates Poisson structures ${\Theta }^{ab}(x)$, as well as non-linear ones, and obtain explicit expressions for all proposed constructions. Our model is unique up to invertible field redefinitions and coordinate transformations.

arXiv comment25 pages; published version

References in corpus (38)

• String Theory and Noncommutative Geometry
• Deformation quantization of Poisson manifolds, I
• D-branes and Deformation Quantization
• Gauge Theory on Noncommutative Spaces
• Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces
• Nonassociative Star Product Deformations for D-brane Worldvolumes in Curved Backgrounds
• Symplectic structures associated to Lie-Poisson groups
• Symmetry, Gravity and Noncommutativity
• T-duality and closed string non-commutative (doubled) geometry
• Nonassociative Gravity in String Theory?
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Gauge theories on the kappa-Minkowski spacetime
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Electrodynamics on $\kappa$-Minkowski space-time
• Hydrogen atom on curved noncommutative space
• Noncommutative field theory on ${\mathbb{R}}_{\lambda }^3$
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Twist to close
• Noncommutative field theory from angular twist
• Star products made (somewhat) easier
• Laplace-Runge-Lenz vector in quantum mechanics in noncommutative space
• A twisted look on kappa-Minkowski: U(1) gauge theory
• Noncommutative $R^d$ via closed star product
• Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry
• Observables and Dispersion Relations in k-Minkowski Spacetime
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• Non-commutative deformation of Chern-Simons theory
• On the Uniqueness of L${}_{\infty }$ bootstrap: Quasi-isomorphisms are Seiberg-Witten Maps
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• $k$-Minkowski-deformation of $U(1)$ gauge theory
• Symplectic realisation of electric charge in fields of monopole distributions
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Noncommutative gauge theories on D-branes in non-geometric backgrounds
• A novel approach to non-commutative gauge theory
• $L_{\infty }$-Bootstrap Approach to Non-Commutative Gauge Theories
• Recurrence relations for symplectic realization of (quasi)-Poisson structures
• Open-String Non-Associativity in an R-flux Background

Cited by in corpus (12)

• Gauge theories on quantum spaces
• Braided Symmetries in Noncommutative Field Theory
• Poisson gauge models and Seiberg-Witten map
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• On Poisson Electrodynamics With Charged Fields
• On the L${}_{\infty }$ structure of Poisson gauge theory
• Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Light Propagation in $\kappa$-Minkowski Space-Time: Gauge Ambiguities and Invariance
• Hamiltonian analysis in Lie-Poisson gauge theory
• Symplectic realization of generalized Snyder-Poisson algebra
• Four-dimensional noncommutative deformations of $U(1)$ gauge theory and $L_{\infty }$ bootstrap