Noncommutative gauge theories and Lorentz symmetry

TL;DR

This paper investigates the conditions under which noncommutative gauge theories can preserve Poincare invariance, clarifying the role of spacetime symmetries in both commutative and noncommutative frameworks.

Contribution

It provides explicit criteria for Poincare invariance in noncommutative gauge theories using a Noether-like approach, and establishes compatibility between commutative and noncommutative descriptions.

Findings

Poincare invariance can be preserved with appropriate interpretation.

Criteria for spacetime symmetry preservation are derived.

Compatibility between commutative and noncommutative formulations is demonstrated.

Abstract

We explicitly derive, following a Noether-like approach, the criteria for preserving Poincare invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that, interpreted appropriately, Poincare invariance holds. The analysis is performed in both the commutative as well as noncommutative descriptions and a compatibility between the two is also established.