Worldline instantons and pair production in inhomogenous fields

We show how to do semiclassical nonperturbative computations within the worldline approach to quantum field theory using “worldline instantons.” These worldline instantons are classical solutions to the Euclidean worldline loop equations of motion, and are closed spacetime loops parametrized by the proper time. Specifically, we compute the imaginary part of the one-loop effective action in scalar QED using “worldline instantons” for a wide class of inhomogeneous electric field backgrounds. We treat both time-dependent and space-dependent electric fields and note that temporal inhomogeneities tend to shrink the instanton loops, while spatial inhomogeneities tend to expand them. This corresponds to temporal inhomogeneities tending to enhance local pair production, with spatial inhomogeneities tending to suppress local pair production. We also show how the worldline instanton technique extends to spinor QED.