Propagating modes of a non-Abelian tensor gauge field of second rank

Abstract

In the non-Abelian tensor gauge field theory a lower-rank field is represented by a general nonsymmetric tensor and describes the propagation of charged bosons of helicities two and zero. We clarify and prove this result from different perspectives which would include generalized Bianchi identities and the analysis of the corresponding partial differential equation. We suggest a new method for counting propagating modes in general gauge field theories. We derive also the expression for the energy–momentum tensor and confirm that its nonzero components get contribution only from helicity-two and helicity-zero states. We extended this analysis considering the interaction between two currents caused by the exchange of a tensor gauge field and proved that the residue at the pole is the sum of three terms each of which describes positive norm polarizations of helicity-two and helicity-zero bosons.