Dimensional regularization of massless quantum electrodynamics in spherical spacetime

The quantization and renormalization of massless electrodynamics in a spacetime of constant curvature are discused. A formalism is presented which is valid in an arbitrary number of dimensions and therefore allows the use of dimensional regularization. In the discussion of the photon propagator it is found that anomalous mass terms dependent on the curvature arise, although these vanish in four dimensions. Further, the gauge-fixing term in the Lagrangian has the unconventional feature of not being a perfect square. The renormalizability of the theory is then demonstrated to one loop order, and the renormalization constants are shown to retain their flat spacetime values. Finally, expansions for the renormalized electron and photon propagators in terms of appropriate spherical harmonics are derived.