We investigate the FLPR model in a recently proposed framework of BRST-related symmetries and perform its full functional quantization as a gauge invariant system taking into account the Gribov ambiguity issue. We obtain a family of BRST-related transformations generated by the discrete group of symmetries of the action. We show that gauges possessing Gribov ambiguities lead to a violation of the initial discrete group of symmetries of the gauge-fixed action.
The FLPR model can be cast into the authors recent framework of BRST-related symmetries, providing full control over the generation of BRST-related symmetries and elucidating how different gauge-fixing choices affect the realization of discrete symmetries of the quantum action. Gauge-fixings with Gribov ambiguites violate the larger discrete symmetries group algebra restricting the possibilities for the BRST-related transformations.
A comparative discussion sheds light into similar issues in QCD.
Hence, we reinforce the importance of a careful analysis of the group algebra of discrete symmetries of the quantum action, including the ghost sector, for general theories in the broader scope of quantum field theory, in terms of functional quantization approaches.