Schwinger Mechanism in the Presence of Arbitrary Time Dependent Background Electric Field

TL;DR

This paper derives an exact, non-perturbative formula for charged scalar pair production in arbitrary time-dependent electric fields, showing the result depends only on the instantaneous field value, not its derivatives.

Contribution

It provides the first exact evaluation of the Schwinger mechanism for arbitrary time-dependent electric fields using path integral methods.

Findings

Exact non-perturbative pair production probability derived

Result independent of all derivatives of E(t)

Functional dependence on E(t) similar to constant field case

Abstract

We study, for the first time, the Schwinger mechanism for the pair production of charged scalars in the presence of an arbitrary time-dependent background electric field E(t) by by directly evaluating the path integral. We obtain an exact non-perturbative result for the probability of charged scalar particle-antiparticle pair production per unit time per unit volume per unit transverse momentum (of the particle or antiparticle) from the arbitrary time dependent electric field E(t). We find that the exact non-perturbative result is independent of all the time derivatives d^nE(t)/dt^n, where n=1,2,....\infty. This result has the same functional dependence on E as the constant electric field E result with the replacement: E -> E(t).