Exact results for effective Lagrangians

A simple method is presented for the evaluation in quantum field theory of the effective Lagrangian induced by one-loop quantum effects. Exact solutions may be obtained in the quasilocal situation where the resulting Lagrangian is allowed to depend on the fields and their first derivatives (and, in some cases, their second derivatives as well). The method is a general one and may be applied to any given field theory. For example, Schwinger's result for the effective Maxwell Lagrangian with constant external field and the Coleman-Weinberg results for effective potentials each emerge as special cases of the general method. By isolating the divergent part of the induced Lagrangian in the general case, moreover, one may recover the 't Hooft-Veltman expression for the one-loop counterterms of an arbitrary field theory. At no stage need Feynman diagrams be evaluated.