Schwinger Mechanism for Fermion Pair Production in the Presence of Arbitrary Time Dependent Background Electric Field

TL;DR

This paper derives an exact, non-perturbative formula for fermion pair production in arbitrary time-dependent electric fields, showing the result depends only on the field itself, not its derivatives, extending Schwinger's original constant field analysis.

Contribution

The paper provides a novel exact formula for fermion pair production in arbitrary time-dependent electric fields, independent of derivatives of the field, generalizing Schwinger's constant field result.

Findings

Exact non-perturbative probability formula derived

Result independent of all derivatives of E(t)

Functional dependence similar to Schwinger's original result

Abstract

We study the Schwinger mechanism for the pair production of fermions in the presence of an arbitrary time-dependent background electric field E(t) by directly evaluating the path integral. We obtain an exact non-perturbative result for the probability of fermion-antifermion pair production per unit time per unit volume per unit transverse momentum (of the fermion or antifermion) from the arbitrary time dependent electric field E(t) via Schwinger mechanism. 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 Schwinger's constant electric field E result with the replacement: E -> E(t).