Derivative expansion of the effective action

This paper describes some methods for calculating derivative terms in the one loop effective action for a quantum field theory. The functional approach and background field method are first used to derive the general form of the one loop determinant. Then the determinant is expanded in powers of derivatives of the background fields. The form of this expansion is described for the simple case of an interacting scalar field, and then for the more complicated problem of a non-abelian gauge field. Finally, the expansion is applied to the task of calculating Higgs mass dependent effects in the Glashow-Weinberg-Salam model, and all terms which grow with the Higgs mass M/sub H/ are found in the one loop approximation. The result of this calculation is used to find the dependence of the gauge boson mass ratio rho on M/sub H/, and also to estimate the size of corrections to W and Z scattering theorems