Canonical Functional Quantization of Pseudo-Photons in Planar Systems

TL;DR

This paper introduces a extended electromagnetism theory with pseudo-photons, applies dimensional reduction to a planar system, and performs canonical quantization, potentially impacting the understanding of Hall systems and magnetic monopoles.

Contribution

It develops a $U_e(1) imes U_g(1)$ electromagnetism framework with pseudo-photons and applies canonical quantization in planar systems, addressing limitations of standard Maxwell theory.

Findings

Formulation of a $U_e(1) imes U_g(1)$ theory with pseudo-photons.

Dimensional reduction to a Maxwell-BF type theory.

Application of canonical quantization to planar systems.

Abstract

Extended $U_e(1)\times U_g(1)$ electromagnetism containing both a photon and a pseudo-photon is introduced at variational level and is justified by the violation of the Bianchi identities in conceptual systems, either in the presence of magnetic monopoles or non-regular external fields, not being accounted by the standard Maxwell Lagrangian. It is carried a dimensional reduction that renders a $U_e(1)\times U_g(1)$ Maxwell-BF type theory and it is considered canonical functional quantization in planar systems which may be relevant in Hall systems.