Translational groups as generators of gauge transformations

TL;DR

This paper explores how translational groups generate gauge transformations in various gauge theories, highlighting their limitations and extensions through Stuckelberg mechanisms, with detailed examples in 3+1 dimensions.

Contribution

It demonstrates the partial gauge generation by translational groups and introduces their role in Stuckelberg extended theories, including explicit examples and reducibility analysis.

Findings

Translational groups generate only a subset of gauge transformations.

Stuckelberg mechanisms extend massive gauge theories to include gauge invariance.

Explicit examples in 3+1 dimensions illustrate the concepts.

Abstract

We examine the gauge generating nature of the translational subgroup of Wigner's little group for the case of massless tensor gauge theories and show that the gauge transformations generated by the translational group is only a subset of the complete set of gauge transformations. We also show that, just like the case of topologically massive gauge theories, translational groups act as generators of gauge transformations in gauge theories obtained by extending massive gauge noninvariant theories by a Stuckelberg mechanism. The representations of the translational groups that generate gauge transformations in such Stuckelberg extended theories can be obtained by the method of dimensional descent. We illustrate these with the examples of Stuckelberg extended first class versions of Proca, Einstein-Pauli-Fierz and massive Kalb-Ramond theories in 3+1 dimensions. A detailed analysis of the partial gauge generation in massive and massless 2nd rank symmetric gauge theories is provided. The gauge transformations generated by translational group in 2-form gauge theories are shown to explicitly manifest the reducibility of gauge transformations in these theories.