Restrictions on the applicability of zeta-function regularization in gauge theories

zeta-function regularization and its extension to higher-loop orders, ''operator regularization,'' have been proposed as a universal, symmetry-preserving regularization scheme for Green's functions in quantum field theory. It is shown here that in gauge theories zeta-function regularization in general violates Becchi-Rouet-Stora (BRS) symmetry, unless a background-field covariant gauge choice enforces full gauge invariance of the quantum effective action. This is exemplified in the case of the Yang-Mills vacuum polarization. Moreover, the connection of zeta-function regularization to dimensional regularization schemes is investigated, and it is found that under certain, frequently recurring circumstances zeta-function regularization gives the same results as dimensional reduction in conjunction with modified minimal subtraction