Revisiting the Fradkin-Vilkovisky Theorem

TL;DR

This paper critically reassesses the Fradkin-Vilkovisky theorem, highlighting its limitations in nonperturbative gauge theory quantization and providing a criterion for gauge fixing admissibility that aligns with known counterexamples.

Contribution

It identifies fundamental reasons why the theorem's usual statement fails nonperturbatively and offers a new criterion for gauge fixing admissibility in simple gauge invariant systems.

Findings

The theorem's independence claim does not hold nonperturbatively.

A criterion for gauge fixing admissibility is established.

Counter-examples support the revised understanding of the theorem.

Abstract

The status of the usual statement of the Fradkin-Vilkovisky theorem, claiming complete independence of the Batalin-Fradkin-Vilkovisky path integral on the gauge fixing "fermion" even within a nonperturbative context, is critically reassessed. Basic, but subtle reasons why this statement cannot apply as such in a nonperturbative quantisation of gauge invariant theories are clearly identified. A criterion for admissibility within a general class of gauge fixing conditions is provided for a large ensemble of simple gauge invariant systems. This criterion confirms the conclusions of previous counter-examples to the usual statement of the Fradkin-Vilkovisky theorem.