Example of Schwinger's modified propagation function

Abstract

The aim of this paper is to investigate a specific example of the two-point-function expression, as proposed in source theory by Schwinger, which represents the inverse modified propagation function as a spectral form. Since this expression for the propagation function most naturally (but not exclusively) refers to spin-1 particles, our program is explicitly carried out in the context of spin-1 electrodynamics, with the progagation function referring to the charged particle. The two-point transverse and longitudinal spectral weight functions are calculated in lowest order. We find that the inclusion of those contributions due to source radiation leads to spectral forms which are infrared-convergent and have non-negative spectral weight functions. Furthermore, the spectral integrals are explicitly evaluated and we see the expected rate of falloff, faster than $\frac{1}{{p}^{2}}$, of the propagation function at large ${p}^{2}$. The complex ${p}^{2}$ poles of the propagation function are large and shown to be physically acceptable within the framework of source theory. We also demonstrate that these results remain unaffected when magnetic and quadrupole couplings are present.