In-in worldline formalism in pair creating fields

TL;DR

This paper develops a comprehensive in-in formalism for pair creation in strong-field QED using worldline methods, enabling all-order calculations of in-in observables and providing a new perspective on vacuum instability and pair production.

Contribution

It introduces an in-in framework based on worldline representation for pair creating fields, facilitating all-order calculations and a first-quantized understanding of N-pair creation.

Findings

Derived all-order in-in formalism for pair creation

Identified non-local interaction insertions in in-in partition functions

Provided an exact first-quantized definition of N-pair creation

Abstract

An in-in framework under Schwinger pair creating fields in strong-field quantum electrodynamics is formulated using in-out propagators in coordinate space, that have first-quantized or worldline representation. The framework is derived to all orders in the background field coupling from both the Bogoliubov coefficient method and Schwinger-Keldysh closed-time path formalism. In-out matrix elements in pair creating fields are readily handled using first-quantized methods, and the approach we develop serves to facilitate the evaluation of in-in observables in pair creating backgrounds. We find that in-in augmentations to the in-out partition function and or propagator amount to the insertion of a non-local interaction term that sandwiches a function that serves to enclose singularities in complex Schwinger propertime. Furthermore, we show the resummation of the in-in partition function leading to vacuum non-persistence that en-route gives an exact first-quantized definition of creating $N$-pairs.