Operator regularization and the divergence of the supercurrent

Operator regularization is introduced as a procedure to compute Green's functions perturbatively. At the one-loop level the effective action is regularized by means of the zeta-function. A perturbative expansion due to Schwinger allows one to compute from the zeta-function one-loop one-particle irreducible Green's Functions. By regulating in this way, we do not have to compute Feynman diagrams, the authors avoid having to introduce a regulating parameter into the initial Lagrangian and they do not encounter any divergent integrals. This procedure is illustrated for N=1 super Yang-Mills theory in which the one-loop one-particle irreducible Green's function associated with the decay of the supercurrent into a vector and a spinor particle is treated. Gauge invariance is automatically maintained and the usual anomaly in the divergence of the supercurrent is recovered