Isospin Invariance and the Vacuum Polarization Energy of Cosmic Strings

TL;DR

This paper confirms that the spectral approach for calculating the vacuum polarization energy of cosmic strings is gauge invariant, by demonstrating the invariance of single particle energies under isospin transformations and the cancellation of non-invariant regularization effects.

Contribution

It provides numerical verification that the spectral method's vacuum energy calculation remains gauge invariant through isospin symmetry considerations.

Findings

Spectral approach is corroborated for vacuum energy calculations.

Gauge invariance is maintained despite regularization procedures.

Numerical evidence shows cancellation of non-invariant effects.

Abstract

We corroborate the previously applied spectral approach to compute the vacuum polarization energy of string configurations in models similar to the standard model of particle physics. The central observation underlying this corroboration is the existence of a particular global isospin transformation of the string configuration. Under this transformation the single particle energies of the quantum fluctuations are invariant, while the inevitable implementation of regularization and renormalization requires operations that are not invariant. We verify numerically that all such variances eventually cancel, and that the vacuum polarization energy obtained in the spectral approach is indeed gauge invariant.