Vacuum Polarization Energy for General Backgrounds in One Space Dimension

TL;DR

This paper introduces an efficient method to calculate the vacuum polarization energy for static field configurations in one-dimensional quantum field theories, especially when traditional symmetry-based decompositions are not possible.

Contribution

It presents a novel computational approach applicable to general backgrounds and mass asymmetries, demonstrated through the $ ext{phi}^6$ kink soliton example.

Findings

Method effectively computes vacuum energies without symmetric channel decomposition.

Vacuum energy depends on soliton position due to mass differences at spatial infinities.

Application to the $ ext{phi}^6$ model shows the method's practical utility.

Abstract

For field theories in one time and one space dimensions we propose an efficient method to compute the vacuum polarization energy of static field configurations that do not allow a decomposition into symmetric and anti--symmetric channels. The method also applies to scenarios in which the masses of the quantum fluctuations at positive and negative spatial infinity are different. As an example we compute the vacuum polarization energy of the kink soliton in the $\phi^6$ model. We link the dependence of this energy on the position of the soliton to the different masses.