2026/04/10 by O. Abla, M. J. Neves
#hep-th
Poisson electrodynamics is the semiclassical limit of the full U(1) non-commutative gauge theory, also known in recent literature as Poisson gauge theory. Two consolidated models for the theory studied in recent years, with a specific choice of non-commutative parameter, Lie-Poisson structures and constant ones, the later also known as the canonical, or Heisenberg case. In this paper, we present the theory considering the new building blocks related to symmetries and conservation laws, as a first step toward understanding the necessary mathematical tools to uncover some of the unknown pieces. We consider non-interacting examples of pure gauge fields, and classical Poisson field theories, related with real and complex scalar fields, as well as fermionic fields, using a constant spacelike deformation parameter. We show that the non-relativistic limit for the non-commutative Dirac equation introduces an orbital Zeeman coupling term for the fermionic fields, and the energy shift in the first excited state depends exclusively on the non-commutative parameter.