1997/01/31 by F. G. Scholtz, F G Scholtz, Sergei V. Shabanov +1 · 1 citation
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Non-Hermitian Physics #Quantum and electron transport phenomena #hep-th
paper · pdf · doi:10.1006/aphy.1997.5754
published as Annals Phys. 263 (1998) 119-132 · 9 pages, Revtex, A better formulation of the conditions on the gauge fixing fermion is given, Several relevant references are added, To appear in Ann. Phys. (N.Y.)
arxiv created 1997/11/26 · openalex publication_date 1998/02/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We investigate the way in which the Gribov problem is manifested in the BRST quantization of simple quantum mechanical models by comparing models with and without a Gribov problem. We show that the hermiticity and nilpotency of the BRST charge together with the Batalin-Vilkovisky theorem yield non-trivial supplementary conditions on gauge fixing fermions. If the gauge fixing fermion satisfies the supplementary conditions, the BRST physical states form a space isomorphic to the Dirac space, 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 restrictions 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-Vilkovisky theorem on the space of Dirac states and implies a breakdown of unitarity and a general dependence of physical quantities on the gauge condition.