On BRST-related symmetries in the FLPR model with Gribov ambiguities

With the recent revival of interest in the FLPR model, novel features have been reported in the literature. A connection between those new feautures and 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 and produce a consistent generating functional which can be used as a starting point for the Gribov-Zwanziger-Sorella program. 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.