# Emerging Translational Variance: Vacuum Polarization Energy of the $\mathbf{\phi^6}$ kink

## TL;DR

This paper introduces an efficient method for calculating the vacuum polarization energy of static field configurations, exemplified by the $ ext{phi}^6$ kink, highlighting how mass differences at spatial infinities influence energy dependence.

## Contribution

It presents a novel computational approach for vacuum polarization energy in models lacking symmetric channel decomposition, applied specifically to the $ ext{phi}^6$ kink.

## Key findings

- Vacuum polarization energy depends on the kink's position due to mass differences at infinities.
- The method effectively handles configurations without symmetric and anti-symmetric channel separation.
- Application to the $ ext{phi}^6$ model demonstrates the approach's utility.

## Abstract

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 in one space dimension. In particular 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 center of the soliton to the different masses of the quantum fluctuations at negative and positive spatial infinity.