BRST symmetric formulation of a theory with Gribov-type copies

A path integral with BRST symmetry can be formulated by summing the Gribov-type copies in a very specific way if the functional correspondence between tau and the gauge parameter omega defined by tau(x) = f(A(mu)(omega)) is ''globally single valued'', where f(A(mu)(omega)) = 0 specifies the gauge condition. A soluble gauge model with Gribov-type copies recently analyzed by Friedberg, Lee, Pang and Ren satisfies this criterion. A detailed BRST analysis of the soluble model proposed by the above authors is presented. The BRST symmetry, when consistently implemented, ensures the gauge independence of physical quantities. In particular, the vacuum (ground) state and the perturbative corrections to the ground state energy in the above model are analyzed from a view point of BRST symmetry and R(xi)-gauge. Possible implications of the present analysis on some aspects of the Gribov problem in non-Abelian gauge theory, such as the 1/N expansion in QCD and also the dynamical instability of BRST symmetry, are briefly discussed.