One-Loop Quantum Energy Densities of Domain Wall Field Configurations

TL;DR

This paper presents a straightforward method for calculating one-loop quantum energy densities of static, single-coordinate-dependent field configurations, especially domain walls, by relating functional determinants to differential equation solutions, simplifying divergence handling.

Contribution

It introduces a novel, simplified procedure for computing quantum energies of domain wall configurations that avoids zero-point summation and facilitates divergence regularization.

Findings

Applied method to 2D $$ theory and 3D scalar electrodynamics.

Successfully isolated and extracted ultraviolet divergences.

Demonstrated approach's effectiveness in specific models.

Abstract

We discuss a simple procedure for computing one-loop quantum energies of any static field configuration that depends non-trivially on only a single spatial coordinate. We specifically focus on domain wall-type field configurations that connect two distinct minima of the effective potential, and may or may not be the solutions of classical field equations. We avoid the conventional summation of zero-point energies, and instead exploit the relation between functional determinants and solutions of associated differential equations. This approach allows ultraviolet divergences to be easily isolated and extracted using any convenient regularization scheme. Two examples are considered: two-dimensional $\phi^4$ theory, and three-dimensional scalar electrodynamics with spontaneous symmetry breaking at the one-loop level.