GRIBOV VERSUS BRST

We investigate the way in which the Gribov problem is manifested in th e BRST quantization of simple quantum mechanical models by comparing m odels with and without a Gribov problem. We show that the hermiticity and nilpotency of the BRST charge together with the Batalin-Vilkovisky theorem yield nontrivial supplementary conditions on gauge fixing fer mions. If the gauge fixing fermion satisfies the supplementary conditi ons, the BRST physical states form a space isomorphic to the Dirac spa ce, and the BRST formal path integral does not suffer from the Gribov problem. The conventional gauge fixing fermion, that gives rise to the Faddeev-Popov integral, fails to satisfy the supplementary conditions due to the Gribov problem. Alternatively, enforcing the conventional gauge fixing fermion, these supplementary conditions imply restriction s on the BRST physical states for which the Batalin-Vilkovisky theorem holds. We find that these BRST physical states are not isomorphic the Dirac states. This can be interpreted as a violation of the Batalin-V ilkovisky theorem on the space of Dirac states and implies st breakdow n of unitarity and a general dependence of physical quantities on the gauge condition. (C) 1998 Academic Press.