Worldline instantons and pair production in inhomogenous fields

Abstract

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.

Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields

“…In this case b = 0, we get x * 1 = artanh(γ k )/k and all the integrals can be carried our analytically, yielding the same results as for a static Sauter pulse, see, e.g., [55]. If the frequency exceeds this threshold value γ ω > γ crit ω , on the other hand, the instanton trajectory is reflected at the poles (i.e., b > 0) and thus the instanton action (4.2) is reduced by the weak temporal pulse ∝ E , leading to a significant enhancement of the pair creation probability.…”

“…Let us start with a brief review of the world-line instanton method, see, e.g., [52][53][54][55][56][57][58][59][60]. Since the electron spin does not affect the exponent of the pair creation probability [55], we consider the vacuum persistence amplitude of scalar QED…”

“…Since the electron spin does not affect the exponent of the pair creation probability [55], we consider the vacuum persistence amplitude of scalar QED…”

“…The first line (valid below and at threshold γ ω ≤ γ crit ω ) is just the result in the static case (see, e.g., [55]). For γ k = 0, we recover Schwinger's result [5] for a constant field (1.1).…”

“…1 In the following, we venture a first step into this direction and employ the worldline instanton technique (see, e.g., [52][53][54][55][56][57][58][59][60]) in order to study the superposition of a spatial and a temporal field pulse as an example for a genuinely space-time dependent field.…”