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Published Online: 04 June 1998

Spatial topology and Yang–Mills vacua

Journal of Mathematical Physics 23, 1668 (1982); https://doi.org/10.1063/1.525552
C. J. Isham and G. Kunstatter
more...View Affiliations
  • Blackett Laboratory, Imperial College, London SW7 2BZ, England
Abstract
We study the canonical vacuum structure of Yang–Mills theories defined on an arbitrary (nonsimply connected) three‐space. We find that the presence of flat Yang–Mills connections with a nontrivial (discrete) holonomy group has profound consequences at the quantum level. In particular, such connections may lead to either an increase or a decrease in the number of quantum vacuum sectors. Our method consists of finding a representation for the space of classical zero‐energy field configurations in terms of a function space D. A simple assumption concerning the physical equivalence of these classical configurations then permits a formal classification of the quantum vacua by the zeroth homotopy set π0(D). Significant progress is made in the analysis of π0(D) for arbitrary three‐spaces and gauge groups, and several specific questions concerning the vacuum states and their diagonalization are answered.

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