The electromagnetic field in Poisson gauge theory: the groupoidal approach
Fabio Di Cosmo, Vladislav G. Kupriyanov, Patrizia Vitale
Published: 2025/10/6
Abstract
We consider the problem of defining the field strength of abelian potentials when the spacetime is a Poisson manifold, within the groupoidal approach. The natural definition in terms of gauge invariant momenta is proved to be equivalent to covariant and invariant tensors of a local symplectic groupoid representing a symplectic realization of the Poisson manifold. A Poisson Chern-Simons model is then proposed and its equations of motion are shortly discussed.