TL;DR
This paper develops a gauge-invariant framework for noncommutative field theories by introducing tools like integration measures and covariant derivatives on the space of star products, revealing new degrees of freedom.
Contribution
It introduces a gauge-invariant approach to noncommutative field theories by formalizing integration measures and covariant derivatives on the space of star products, enabling a more consistent treatment.
Findings
Covariant derivatives can be expressed via connections, introducing new degrees of freedom.
A gauge-invariant formulation of star product realizations is achieved.
Tools for integration and differentiation on the space of star products are developed.
Abstract
The choice of a star product realization for noncommutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as integration measures and covariant derivatives on this space. The covariant derivative can be expressed in terms of connections in the usual way giving rise to new degrees of freedom for noncommutative theories.
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