SUPERMATRIX PROPER-TIME REPRESENTATION OF ONE-LOOP EFFECTIVE ACTION AND GAUGE-INVARIANCE

Starting from the supermatrix proper-time representation, we construct the gauge-invariant one-loop effective action for generic renormalizable field theories involving spin-0, -, and -1 fields in flat or curved spacetime. In the presence of fermion couplings involving the 5 matrix (but the theory having no genuine gauge anomaly), gauge invariance requires that the usual ultraviolet renormalization procedure be supplemented by appropriate finite renormalization terms. The supermatrix method is very convenient for finding the finite renormalization terms associated with vertex functions involving some external fermion legs. © 1990 The American Physical Society.