Exact instantons via worldline deformations

TL;DR

This paper introduces a novel deformation technique to construct exactly solvable worldline instanton models, enabling efficient computation of quantum tunneling effects in nonstatic backgrounds.

Contribution

It presents a new method to generate infinitely many exactly solvable models for worldline instantons using deformation functions, expanding the toolkit for quantum field theory calculations.

Findings

Validates the technique on known cases of Schwinger pair creation.

Demonstrates the method's ability to produce new solvable models.

Provides explicit examples of tunneling exponential calculations.

Abstract

The imaginary part of the one loop effective action in external backgrounds can be efficiently computed using worldline instantons which are closed periodic paths in spacetime. Exact solutions for nonstatic backgrounds are only known in certain cases. In this paper, we propose a novel technique allowing the construction of further exactly solvable models. In order to do so, we introduce a deformation function which maps the worldline instantons for a given model to the closed periodic stationary paths of a new model. Executing this procedure iteratively results in a chain of infinitely many solvable models. Similar ideas were applied to topological and nontopological defects in quantum field theory. We explicitly discuss the tunneling exponential in the Schwinger pair creation rate and illustrate the validity of the proposed technique for well-known cases.