Quantum Mechanics On Spaces With Finite Fundamental Group
Quantum Physics
2007-05-23 v1 General Relativity and Quantum Cosmology
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 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.
Cite
@article{arxiv.quant-ph/9508011,
title = {Quantum Mechanics On Spaces With Finite Fundamental Group},
author = {Domenico Giulini},
journal= {arXiv preprint arXiv:quant-ph/9508011},
year = {2007}
}
Comments
40 Pages, Plain-TeX, no figures