We pursue operator regularization beyond lowest order. In lowest order, it is the determinants of operators that are regulated; beyond lowest order it is the inverses of operators. As in lowest order, operator regularization to two-loop order and beyond avoids explicit infinities both in the integrals that are evaluated and in the regulating parameter s as it approaches its limiting value of zero. Operator regularization also replaces the Feynman diagrammatic expansion with an expansion due to Schwinger. No explicit symmetry-breaking regulating parameter is inserted into the original Lagrangian. We illustrate our technique by examining the two-point function in [Formula: see text] scalar theory, the effective potential in [Formula: see text] scalar theory, the vacuum polarization in massless quantum electrodynamics, and the two-point function in the Wess–Zumino model using both the superfield and component-field formalism. In all cases we find expressions that are divergence free and remain finite as the regulating parameter approaches its limiting value. In the final model we explicitly show that the supersymmetry Ward identity for the two-point functions is satisfied to two-loop order.

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The Becchi–Rouet–Stora (BRS) invariance of quantum electrodynamics in the nonlineart' Hooft–Veltman gauge ∂∙A + λA2 = 0 is examined. It is the longitudinal contribution to the vacuum polarization in the t' Hooft–Veltman gauge that upholds BRS invariance.

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