Abstract
By using supermatrices and the super-Fredholm determinant, the Schwinger-DeWitt propertime expansion method is generalized to the case with background Fermi fields as well as background Bose fields. For quantum field theories defined in flat or curved space-time, we present a derivation of complete one-loop renormalization counterterms (including those involving Fermi fields) by this method. The whole one-loop counterterms are given in terms of the supertrace of a single coefficient a 2 - a supermatrix - appearing in the DeWitt-WKB expansion.
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