Schwinger Pair Production in SL$(2,\mathbb{C})$ Topologically Non-Trivial Fields via Non-Abelian Worldline Instantons

TL;DR

This paper extends the worldline instanton method to analyze Schwinger pair production in complex, non-Abelian gauge fields, revealing decay phenomena in complex instanton backgrounds where pair production was previously unpredicted.

Contribution

It introduces a non-Abelian worldline instanton approach for SL(2,C) fields, providing new insights into pair production in complex gauge backgrounds.

Findings

Pair production not observed in BPST instanton

Complex extension of BPST instanton decays via Schwinger effect

Method applicable to complex non-Abelian gauge fields

Abstract

Schwinger pair production is analyzed in a BPST instanton background and in its SL$(2,\mathbb{C})$ complex extension for complex scalar particles. A non-Abelian extension of the worldline instanton method is utilized, wherein Wong's equations in a coherent state picture adopted for SL$(2,\mathbb{C})$ are solved in Euclidean spacetime. While pair production is not predicted in the BPST instanton, a complex extension of the BPST instanton, existing as parallel fields in Minkowski spacetime, is shown to decay via the Schwinger effect.