TOPOLOGICAL STUDY OF GLOBAL QUANTIZATION IN NON-ABELIAN GAUGE THEORIES AND THE OPEN UNIVERSE

Abstract

We study some topological aspects of non-Abelian gauge theories intimately connected with the Lie algebras of the gauge groups and the homotopy theory in the generalized gauge orbit space. The physics connection with the nonperturbative solution to the strong CP problem by magnetic monopoles and the quantization rule for the effective vacuum angle as originally proposed by the author are also discussed. In addition, some relevant topological formulas are given and discussed. We emphasize that a result7 from their physics application is that the usual gauge orbit space on the compactified space may contain at most a Z2 monopole structure in the SP (2N)(N= rank ) gauge theories; such a Z2 structure may induce spontaneous CP violations in SP (2N) gauge theories, as was noted. Some relevance to the open universe is discussed too. It is expected from our results that the open universe in the case of a nonvanishing θ can also be regarded as a quantum effect of the global quantization in the gauge orbit space. We expect that our results will be useful for other studies of non-Abelian gauge theories in general. Some remarks are also given related to our global quantization and the gauge theories in generalized gauge orbit space.