Determinant Calculations with Random Walk Worldline Loops

TL;DR

This paper introduces a method to compute bosonic and fermionic determinants and 1-loop effective actions using statistical evaluation of random walk worldline loops on a lattice, demonstrated through numerical examples.

Contribution

It presents a novel lattice-based stochastic approach to determinant calculations in quantum field theory, extending previous methods.

Findings

Successful numerical calculations for constant gauge fields

Effective demonstration of the method's applicability

Discussion of potential for general field backgrounds

Abstract

We propose to calculate bosonic and fermionic determinants with some general field background, and the corresponding 1-loop effective actions by evaluating random walk worldline loops generated statistically on the lattice. This is illustrated by some numerical calculations for constant gauge field backgrounds and then discussed for the general case.