Derivative Expansion of the Effective Action for Massless Scalar   Electrodynamics in Arbitrary Gauge
  It is shown how operator regularization can be used to obtain an expansion of the effective action in powers of derivatives of the background field. This is applied to massless scalar electrodynamics to find the one-loop corrections to the kinetic terms associated with both the scalar and vector fields in arbitrary gauge. This allows us to examine the radiatively induced masses arising in this model. 
D.G.C. McKeon