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arXiv · hep-th/9306098

Gauge Field, Parity and Uncertainty Relation of Quantum Mechanics on S^1

Shogo Tanimura
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Abstract

We consider the uncertainty relation between position and momentum of a particle on $ S^1 $ (a circle). Since $ S^1 $ is compact, the uncertainty of position must be bounded. Consideration on the uncertainty of position demands delicate treatment. Recently Ohnuki and Kitakado have formulated quantum mechanics on $ S^D $ (a $D$-dimensional sphere). Armed with their formulation, we examine this subject. We also consider parity and find a phenomenon similar to the spontaneous symmetry breaking. We discuss problems which we encounter when we attempt to formulate quantum mechanics on a general manifold.

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Shogo Tanimura. 1993-06-21. Gauge Field, Parity and Uncertainty Relation of Quantum Mechanics on S^1. https://doi.org/10.1143/ptp%2F90.2.271

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