Symmetries and Conservation Laws in Lie-Poisson Electrodynamics
arXiv:2607.04522
The paper studies Lie-Poisson electrodynamics, a non‑Abelian nonlinear deformation of Maxwell theory, showing how a field redefinition maps its dynamics to standard electrodynamics and using this map to construct symmetry generators, conserved currents, and a quantization scheme.
Abstract
Lie-Poisson electrodynamics (LPE) is a non-Abelian and nonlinear deformation of usual electrodynamics, where the gauge algebra is defined through a Lie-algebra-type Poisson bracket on space-time. We focus on the geometric approach to LPE in the absence of charged matter. We establish a non-trivial field redefinition which, under mild technical assumptions, maps the LPE dynamics to that of Maxwell theory. Using this map, for any symmetry of the Maxwell action, we construct generators of LPE symmetries and the corresponding conserved currents. In particular, we obtain deformed Poincaré transformations. We also outline a natural quantization prescription for LPE based on our field redefinition.
slightly extended version, submitted to a peer-reviewed journal, 15 pages