On BRST-Related Symmetries in the FLPR Model with Gribov Ambiguities

Abstract: With a recent revival, novel features of the FLPR model have been reported in the literature. A connection between those features to QCD involving the Gribov problem is explored. 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 ambiguities. 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 obtained results shed light into similar issues in QCD by the corresponding association of variables and fields between the two systems.