Worldline Instantons II: The Fluctuation Prefactor

TL;DR

This paper extends the worldline instanton formalism to include quantum fluctuation prefactors, providing a numerical method and explicit formulas for certain electric fields, improving the accuracy of nonperturbative QED calculations.

Contribution

It introduces a direct numerical approach to compute fluctuation prefactors in the worldline instanton method, with explicit formulas for one-dimensional inhomogeneous electric fields.

Findings

Excellent agreement with WKB and numerical worldline loop results.

Derived explicit formulas for fluctuation prefactors in specific cases.

Enhanced the semiclassical approximation accuracy for QED effective action.

Abstract

In a previous paper [1], it was shown that the worldline expression for the nonperturbative imaginary part of the QED effective action can be approximated by the contribution of a special closed classical path in Euclidean spacetime, known as a worldline instanton. Here we extend this formalism to compute also the prefactor arising from quantum fluctuations about this classical closed path. We present a direct numerical approach for determining this prefactor, and we find a simple explicit formula for the prefactor in the cases where the inhomogeneous electric field is a function of just one spacetime coordinate. We find excellent agreement between our semiclassical approximation, conventional WKB, and recent numerical results using numerical worldline loops.