Particle spectrum of Non-Abelian tensor gauge fields

TL;DR

This paper reviews non-Abelian tensor gauge field theory, analyzing free field equations to identify particle content and propagating modes, highlighting the spectrum of higher rank gauge fields in four-dimensional space-time.

Contribution

It provides a detailed analysis of the particle spectrum and propagating modes of non-Abelian tensor gauge fields, emphasizing the physical relevance in four dimensions.

Findings

Rank-2 gauge field describes helicity-2 and 0 modes.

Rank-3 gauge field describes helicity-3 and doublet of helicity-1 modes.

Higher-dimensional space-times have negative norm states.

Abstract

We present a brief review of the non-Abelian tensor gauge field theory and analyze its free field equations for lower rank gauge fields when the interaction coupling constant tends to zero. The free field equations are written in terms of the first order derivatives of extended field strength tensors similar to the electrodynamics and non-Abelian gauge theories. We determine the particle content of the free field equations and count the propagating modes which they describe. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. Only four-dimensional space-time is physically acceptable, because in five- and higher-dimensional space-time the equation has solutions with negative norm states. We discuss the structure of the particle spectrum for higher rank gauge fields.