Abstract
We describe how inequivalent quantizations (superselection sectors) arise within two related algebraic approaches to quantum mechanics (viz. quantization by canonical groups and by C ∗-algebras). By construction of the quantum hamiltonian and the path integral of a particle moving on a coset space, we show that the inequivalent quantizations manifest themselves as the particle coupling to a certain fictitious external gauge field, in a representation depending on the superselection sector; various well-known topologically non-trivial Yang-Mills field configurations emerge in this way. The general theory is illustrated by taking the coset space to be a circle and a sphere, which puts θ-angles (hence the Aharonov-Bohm effect) and the Dirac charge quantization condition, respectively, in a new light.
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