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

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 ${\varphi }^6$ 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.