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.

25 pages; published version

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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