Безмассовое поле Штюкельберга, точные решения в декартовых координатах и калибровочные степени свободы

Abstract

In the paper we examine the massless Stueckelberg field. Among the eleven field function components, the antisymmetric tensor represents the gauge variables, whereas the scalar and vector correspond to physically observable quantities. It is shown that in Cartesian coordinates the Stueckelberg equations permit the existence of five independent solutions which describe the different states of the field. We have derived an expression for the energy-momentum tensor of the massless Stueckelberg field. We find its explicit form for arbitrary linear combination of five established solutions. We have found four combinations of five solutions which do not contribute to energy-momentum tensor, therefore they correspond to purely gauge states. There exists only one solution which corresponds to nonvanishing energy-momentum tensor, it relates to physically observable states of the massless Stueckelberg field.