Perturbation Theory for Magnetic Monopoles

The Feynman-Dyson perturbation theory is applied to Schwinger's model of the monopole. The propagator for photon exchange between electric and magnetic charges is found to be ${D^{\mathrm{AB}}}_{\mu \nu }\mathrm{}\left(k\right)={({\mathrm{k}}^2+i\epsilon )}^{-1\mathrm{}}\times \frac{\left({\epsilon }_{\mu \nu \lambda \kappa }{n}^{\lambda }{k}^{\kappa }\right)}{\left(n·k\right)}$. [In the frame of quantization, $n=(0, \hat{n})$, where $\hat{n}$ is the unit vector in the direction of the singularity line.] Since the exact theory is independent of $n$, one might try to obtain a manifestly covariant perturbation expansion by averaging over all directions of $n$. Under such a procedure the Born term reproduces the known nonrelativistic limit, if proper care is taken of the helicity-flip phase factor.