Is there a solution to the Rarita-Schwinger wave equation in the presence of an external electromagnetic field?

Abstract

The method of characteristics is applied in order to obtain the retarded Green's function for the Rarita-Schwinger (RS) wave equation coupled minimally to an external electromagnetic field. The retarded Green's function is Taylor expanded in terms of singularities around the characteristic surfaces and the coefficients of singular terms are calculated. In general, when the above method is applied to a hyperbolic partial differential equation, the equations satisfied by the coefficients are singular but compatible in the sense that iteration is possible. In this paper, we shall show that in the case of the RS equation in the presence of an external electromagnetic field, this compatibility does not exist implying that the existence of the solution is doubtful.