One-loop effective Lagrangian for an arbitrary-dimensional field theory with a strong but slowly-varying background field

Abstract

The effective Lagrangian contains, in principle, all the information one can possibly extract from a quantum field theory. However, even up to one-loop approximation, the effective Lagrangian is an extremely difficult quantity to calculate. It requires one to solve a Green function equation whose non-local nature may be handled only by imposing restrictions on the background fields. This non-local problem has led to an industy of approximation schemes.
Recently, a method of calculating the one-loop effective Lagrangian based on the background field approach of Brown and Duff has been developed and applied to gauge theories. This method has extended the results of Brown and Duff beyond the covariantly constant field strength approximation. The resulting Lagrangian, however, accommodates only a limited number of covariant derivatives of the field strength tensor.
In this study, we allow a greater degree of arbitrariness to the background field by relaxing the restriction employed in the recent formulations. Specifically, we allow in the formalism up to the third covariant derivatives of the field strength tensor and derive the corresponding equation satisfied by the Green function from which the one-loop effective Lagrangian can be calculated.