Phys. Rev. Lett. 60, 481–483 (1988)Inequivalent quantizations and fundamentally perfect spacesReceived 22 June 1987; published in the issue dated 8 February 1988 We investigate the problem of inequivalent quantizations of a physical system with multiply connected configuration space X. For scalar quantum theory on X we show that state vectors must be single valued if and only if the first homology group H1(X) is trivial, or equivalently the fundamental group π1(X) is perfect. The θ structure of quantum gauge and gravitational theories is discussed in light of this result. © 1988 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.60.481
DOI:
10.1103/PhysRevLett.60.481
PACS:
03.65.-w, 02.40.+m, 04.60.+n, 11.15.Kc
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