Solution of free field equations in non-Abelian tensor gauge field theory

Abstract

Recently proposed Lagrangian for non-Abelian tensor gauge fields contains quadratic kinetic terms, as well as cubic and quartic terms describing non-linear interaction of tensor gauge fields with dimensionless coupling constant g. We analyze the free field equations for the lower rank non-Abelian tensor gauge fields. These equations are written in terms of the first order derivatives of extended field strength tensors, similarly to the electrodynamics and Yang–Mills theory. 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. We present the free field equation for the general rank-(s+1) tensor gauge field and its higher helicity solution.