Heat kernel approach to the one-loop effective action for nonlinear electrodynamics

A bstract We develop a heat kernel method to compute the one-loop effective action for a general class of nonlinear electrodynamic (NLED) theories in four dimensional Minkowski spacetime. Working in the background field formalism, we extract the logarithmically divergent part of the effective action, the so-called induced action , corresponding to the DeWitt a 2 coefficient of the heat kernel. In NLED, quantisation yields non-minimal differential operators, for which standard heat kernel techniques are not immediately applicable. Considering the weak-field regime, we calculate the a 0 , a 1 and a 2 contributions to leading order in the background electromagnetic field strength. Finally, we consider conformal NLED theories and compute the a 0 contribution to all orders. For this class, we comment on the role of causality being necessary and sufficient for the convergence of the exact a 1 and a 2 contributions.