Gribov Problem and Brst Symmetry †

After a brief historical comment on the study of BRS(or BRST) symmetry , we discuss the quantization of gauge theories with Gribov 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 τ and the gauge parameter ω defined by τ(x) = f(Aμ(x)) is “globally single valued”, where f(A ω μ(x)) = 0 specifies the gauge condition. As an example of the theory which satisfies this criterion, we comment on a soluble gauge model with Gribov-type copies recently analyzed by Friedberg, Lee, Pang and Ren. We also comment on a possible connection of the dynamical instability of BRST symmetry with the Gribov problem on the basis of an index notion. To be published in the Proceedings of International Symposium on BRS Symmetry on the Occasion of its 20th Anniversary, September 18-22, 1995, RIMS, Kyoto University, Kyoto, Japan(Universal Academy Press, Tokyo)