Twist Symmetry and Gauge Invariance

TL;DR

This paper demonstrates that noncommutative gauge theories with twisted Poincaré symmetry are correct when applying twist symmetry properly, clarifying discrepancies with recent approaches to twisted gauge transformations.

Contribution

It clarifies the correct application of twist symmetry in gauge theories and resolves contradictions with recent methods, emphasizing the role of local internal symmetry.

Findings

Noncommutative gauge theories with $igstar$-product possess twisted Poincaré symmetry.

Proper application of twist symmetry confirms the validity of certain noncommutative gauge theories.

Contradictions in recent approaches are due to misinterpretation of gauge fields as arising from local internal symmetry.

Abstract

By applying properly the concept of twist symmetry to the gauge invariant theories, we arrive at the conclusion that previously proposed in the literature noncommutative gauge theories, with the use of $\star$-product, are the correct ones, which possess the twisted Poincar\'e symmetry. At the same time, a recent approach to twisted gauge transformations is in contradiction with the very concept of gauge fields arising as a consequence of {\it local} internal symmetry. Detailed explanations of this fact as well as the origin of the discrepancy between the two approaches are presented.