The Einstein-Maxwell system, Ward identities, and the Vilkovisky construction

TL;DR

This paper investigates gauge fixing dependence in quantum gravity and Maxwell-Einstein theories, analyzing the Vilkovisky-DeWitt construction's effectiveness in removing this dependence and its implications for gauge theories and asymptotic freedom.

Contribution

It extends the Vilkovisky-DeWitt method to general gauges and identifies Ward identity criteria necessary for gauge independence in quantum gravity and gauge theories.

Findings

Vilkovisky-DeWitt construction can remove gauge dependence under specific regularization criteria.

Ward identities impose constraints on regularization schemes to ensure gauge independence.

Results suggest gauge dependence issues in asymptotic freedom calculations involving gravitons.

Abstract

The gauge fixing dependence of the one-loop effective action of quantum gravity in the proper-time representation is investigated for a space of arbitrary curvature, and the investigation is extended to Maxwell-Einstein theory. The construction of Vilkovisky and DeWitt for removal of this depence is then considered in general gauges, and it is shown that nontrivial criteria arising from a Ward identity of the theory must be obeyed by the regularization scheme, if the construction is to remove the gauge dependence of quadratic and quartic divergences. The results apply also to non-Abelian gauge theories; they are used to address the question of gauge dependence of asymptotic freedom arising through internal graviton lines at one-loop order as suggested by Robinson and Wilczek.