Gauge field theories with covariant star-product

TL;DR

This paper develops a noncommutative gauge theory on symplectic manifolds using a covariant star-product, demonstrating gauge covariance of the field strength and invariance of the Yang-Mills action up to second order.

Contribution

It introduces a covariant star-product framework for noncommutative gauge theories on symplectic manifolds, ensuring gauge covariance and invariance properties.

Findings

Field strength two-form is gauge covariant.

Deformed Bianchi identity is satisfied.

Yang-Mills action is gauge invariant up to second order.

Abstract

A noncommutative gauge theory is developed using a covariant star-product between differential forms defined on a symplectic manifold, considered as the space-time. It is proven that the field strength two-form is gauge covariant and satisfies a deformed Bianchi identity. The noncommutative Yang-Mills action is defined using a gauge covariant metric on the space-time and its gauge invariance is proven up to the second order in the noncommutativity parameter.