DELTA(0) DIVERGENCES AND THE FUNCTIONAL-INTEGRATION MEASURE

We show that whenever a theory involves equal numbers of bosonic and fermionic degrees of freedom and Fujikawa's measure is used for each field, then the theory is free of delta(0) divergences at the one loop order. Consequently, in any supersymmetric theory the delta(0) divergences are absent. If a theory involves different numbers of bosonic and fermionic degrees of freedom, then the maximal divergences at the one loop order can be made to vanish by suitably introducing Pauli-Villars regulators or by choosing a nonultralocal, but still unitary, extension of the functional measure. The vanishing of delta(0) divergences is related to the correct normalization of the functional integral.