Gribov Problem and BRST Symmetry

Abstract

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 $\tau$ and the gauge parameter $\omega$ defined by $\tau (x)=f(A_{\mu }^{\omega }(x))$ is ``globally single valued'', where $f(A_{\mu }^{\omega }(x))=0$ 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.

20 pages plus 1 figure. To be published in the Proceedings of International Symposium on BRS Symmetry(Universal Academy Press, Tokyo)