  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.
