Particle spectrum of Non-Abelian tensor gauge fields

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.