Finite temperature regularization

TL;DR

This paper introduces a novel non-perturbative regularization method for Quantum Field Theories by embedding them into a higher-dimensional spacetime with specific boundary conditions, effectively simulating finite-temperature effects.

Contribution

The authors propose a new regularization scheme involving extra compactified dimensions and field doubling, providing a finite-temperature interpretation for fermionic theories.

Findings

Validated in perturbative vacuum polarization calculations.

Confirmed in non-perturbative chiral anomaly analysis.

Demonstrated consistency with known quantum field theory results.

Abstract

We present a non-perturbative regularization scheme for Quantum Field Theories which amounts to an embedding of the originally unregularized theory into a spacetime with an extra compactified dimensions of length L ~ Lambda^{-1} (with Lambda an ultraviolet cutoff), plus a doubling in the number of fields, which satisfy different periodicity conditions and have opposite Grassmann parity. The resulting regularized action may be interpreted, for the fermionic case, as corresponding to a finite-temperature theory with a supersymmetry, which is broken because of the boundary conditions. We test our proposal in a perturbative calculation (the vacuum polarization graph for a D-dimensional fermionic theory) and in a non-perturbative one (the chiral anomaly).