Functional Determinants in Quantum Field Theory

TL;DR

This paper discusses recent progress in extending the Gel'fand-Yaglom method for computing functional determinants from one-dimensional problems to higher-dimensional cases, with applications in quantum field theory.

Contribution

It introduces a novel approach to evaluate functional determinants of partial differential operators in higher dimensions, advancing computational techniques in quantum field theory.

Findings

Extended Gel'fand-Yaglom method to higher dimensions

Simplified computation of functional determinants in quantum field theory

Potential applications in complex quantum systems

Abstract

Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional problems, a classical result of Gel'fand and Yaglom dramatically simplifies the problem so that the functional determinant can be computed without computing the spectrum of eigenvalues. Here I report recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators), with applications in quantum field theory.