Abstract
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 (X) is trivial, or equivalently the fundamental group (X) is perfect. The θ structure of quantum gauge and gravitational theories is discussed in light of this result.
- Received 22 June 1987
DOI:https://doi.org/10.1103/PhysRevLett.60.481
©1988 American Physical Society