Revisiting the Fradkin-Vilkovisky theorem
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 quantization 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.