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Quantum Mechanics On Spaces With Finite Fundamental Group

Domenico Giulini
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Abstract

We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that arise from the non-simply connectedness of the classical configuration space. We define the quantum theory on the universal cover but restrict the algebra of observables $Ø$ to the commutant of the algebra generated by deck-transformations. We apply standard superselection principles and construct the corresponding sectors. We emphasize the relevance of all sectors and not just the abelian ones.

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Domenico Giulini. 1995-08-16. Quantum Mechanics On Spaces With Finite Fundamental Group. https://arxiv.org/abs/quant-ph/9508011

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