Extended BRS algebra and color confinement —Well-definedness ofN a charge

Abstract

We examine the color confinement scheme and its realization proposed by Kugo and Ojima. We first point out that their scheme (in its original naive form) lacks self-consistency at the level of realizations. By using the properties of the extended BRS algebra and considering the well-definedness of the charge operatorNa constituting a part of the global color operator, we then deduce the new confinement conditions in the Landau gauge which replace the K−O condition. We also clarify what kind of ghost structures are suggested by the well-or ill-definedness ofNa. It is shown that there are four possible cancellation mechanisms of ghosts. In particular, it turns out that the octet of ghosts proposed by Nishijima in his confinement theory arises from the well-definedness of theNa charge, whereas the elementary quartet arises from the ill-definedness ofNa.