Non-Abelian tensor gauge fields and extended current algebra. Generalization of Yang-Mills theory

TL;DR

This paper introduces an infinite-dimensional extension of gauge transformations for non-Abelian tensor gauge fields, forming a new algebraic structure that enables a consistent Lagrangian describing massless tensor gauge bosons with enhanced gauge invariance.

Contribution

It generalizes Yang-Mills theory by constructing an extended current algebra and gauge-invariant Lagrangians for tensor gauge fields with improved physical properties.

Findings

Constructed two infinite series of gauge-invariant quadratic forms.

Demonstrated the elimination of negative norm states.

Described massless tensor gauge bosons with specific helicities.

Abstract

We suggest an infinite-dimensional extension of the gauge transformations which includes non-Abelian tensor gauge fields. Extended gauge transformations of non-Abelian tensor gauge fields form a new large group which has natural geometrical interpretation it terms of extended current algebra associated with compact Lie group. We shall demonstrate that one can construct two infinite series of gauge invariant quadratic forms, so that a linear combination of them comprises the general Lagrangian. The general Lagrangian exhibits enhanced local gauge invariants with double number of gauge parameters and allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field. Therefore it describes two polarizations of helicity-two and helicity-zero massless charged tensor gauge bosons.