Closed Algebras for Higher Rank, non-Abelian Tensor Gauge Fields

TL;DR

This paper introduces a systematic method for constructing and classifying gauge transformation algebras for high-rank tensor gauge fields, resulting in the discovery of a new algebra for tensor gauge transformations.

Contribution

It provides a general framework for deriving gauge algebras of arbitrary rank tensor fields and presents a novel algebra not previously known.

Findings

A systematic method for algebra construction is developed.

New algebra for tensor gauge transformations is identified.

Framework recovers known algebras and generates new ones.

Abstract

A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be stated, in a generic way, via an ansatz that contains all the possible terms, with arbitrary coefficients and the maximum number of tensor gauge functions. The requirement for the closure of the algebra will prove to be restrictive, but, nevertheless, leave a variety of choices. Properly adjusting the values of the initial coefficients and imposing restrictions on the gauge functions, one can, one the one hand, recover all the, so far, analysed algebras and on the other, construct new ones. The presentation of a brand new algebra for tensor gauge transformations is the central result of this article.