Non-Abelian Tensor Gauge Fields

TL;DR

This paper explores an extension of Yang-Mills theory incorporating non-Abelian tensor gauge fields, analyzing their particle content, interactions, and a new gauge-invariant density that can generate a mass gap.

Contribution

It introduces a novel non-Abelian tensor gauge field framework with a new gauge-invariant density that provides a gauge-invariant mass for Yang-Mills bosons.

Findings

Tensor gauge fields describe helicity 2, 0, and 3/2 modes.

A new metric-independent gauge invariant density is constructed.

The augmented Lagrangian yields a gauge-invariant mass gap.

Abstract

Recently proposed extension of Yang-Mills theory contains non-Abelian tensor gauge fields. The Lagrangian has quadratic kinetic terms, as well as cubic and quartic terms describing non-linear interaction of tensor gauge fields with the dimensionless coupling constant. We analyze particle content of non-Abelian tensor gauge fields. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity 2 and 0. We introduce interaction of the non-Abelian tensor gauge field with fermions and demonstrate that the free equation of motion for the spin-vector field correctly describes the propagation of massless modes of helicity 3/2. We have found a new metric-independent gauge invariant density which is a four-dimensional analog of the Chern-Simons density. The Lagrangian augmented by this Chern-Simons-like invariant describes massive Yang-Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory.