Poisson gauge models and Seiberg-Witten map

Abstract

The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance in the direction of a further development of the proposed formalism, including the derivation of Noether identities and conservation of currents. For any linear non-commutativity, ${\Theta }^{ab}(x)=f_c^{ab}{x}^c$, with $f_c^{ab}$ being structure constants of a Lie algebra, an explicit form of the gauge Lagrangian is proposed. In particular a universal solution for the matrix $\rho$ defining the field strength and the covariant derivative is found. The previously known examples of $\kappa$-Minkowski, $\lambda$-Minkowski and rotationally invariant non-commutativity are recovered from the general formula. The arbitrariness in the construction of Poisson gauge models is addressed in terms of Seiberg-Witten maps, i.e., invertible field redefinitions mapping gauge orbits onto gauge orbits.

arXiv comment20 pages

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Cited by in corpus (8)

• Gauge theories on quantum spaces
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• On Poisson Electrodynamics With Charged Fields
• 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
• Symplectic realization of generalized Snyder-Poisson algebra