Multiparticle correlations in the Schwinger mechanism

TL;DR

This paper analyzes particle production in the Schwinger mechanism within scalar QED, deriving the multiplicity distribution of created particles under a homogeneous electric field, showing it follows a Bose-Einstein distribution and confirming results with Bogoliubov transformations.

Contribution

It provides a derivation of the particle multiplicity distribution in the Schwinger mechanism using LSZ reduction and confirms the distribution as Bose-Einstein, including explicit solutions for time-dependent fields.

Findings

Particles are produced independently across different momenta.

The multiplicity distribution per mode is Bose-Einstein.

Explicit solutions are provided for specific electric field configurations.

Abstract

We discuss the Schwinger mechanism in scalar QED and derive the multiplicity distribution of particles created under an external electric field using the LSZ reduction formula. Assuming that the electric field is spatially homogeneous, we find that the particles of different momenta are produced independently, and that the multiplicity distribution in one mode follows a Bose-Einstein distribution. We confirm the consistency of our results with an intuitive derivation by means of the Bogoliubov transformation on creation and annihilation operators. Finally we revisit a known solvable example of time-dependent electric fields to present exact and explicit expressions for demonstration.