Trace Anomaly and Quantization of Maxwell's Theory on Non-Commutative Spaces

TL;DR

This paper investigates Maxwell's theory on non-commutative spaces, deriving energy-momentum tensors, their traces, and performing Dirac's quantization to understand the theory's quantum properties.

Contribution

It introduces the canonical and symmetric energy-momentum tensors with non-zero traces and performs Dirac quantization, extending Hamiltonian and equations of motion in a gauge covariant framework.

Findings

Energy-momentum tensors with non-zero traces in non-commutative Maxwell theory

Successful Dirac quantization of the non-commutative Maxwell theory

Extended Hamiltonian and equations of motion in a covariant form

Abstract

The canonical and symmetrical energy-momentum tensors and their non-zero traces in Maxwell's theory on non-commutative spaces have been found. Dirac's quantization of the theory under consideration has been performed. I have found the extended Hamiltonian and equations of motion in the general gauge covariant form.