Localisation in worldline pair production and lightfront zero-modes

TL;DR

This paper demonstrates that pair production in lightfront-dependent electric fields is governed by lightfront zero-modes, with the effective action localizing on these modes and vanishing if they are removed.

Contribution

It reveals that lightfront zero-modes are essential for pair production, providing an exact nonperturbative understanding via the worldline path integral.

Findings

Pair production probability is exactly given by the locally constant approximation.

Contributing paths localize on hypersurfaces of constant lightfront time.

Removing lightfront zero-modes eliminates pair production.

Abstract

The nonperturbative probability of pair production in electric fields depending on lightfront time is given exactly by the locally constant approximation. We explain this by showing that the worldline path integral defining the effective action contains a constraint, which localises contributing paths on hypersurfaces of constant lightfront time. These paths are lightfront zero-modes and there can be no pair production without them; the effective action vanishes if they are projected out.