Quantum mechanics and topology
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Physics defined on multiply connected manifolds is an old topic in theoretical physics. In the context of the path integral formalism it was studded by the first time by Schulman in 1968 and rigorously formulated by Laidlaw and the Witt and Dowker in 1971. The central point is that in a multiply connected manifold the paths have different weights in the sum over histories and the problema - which does not exist in the "standard" quantum mechanicsis how to define a quantum theory taking this fact into account.