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

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

1993-06-21

arxiv.org/abs/hep-th/9306098v1

Prog.Theor.Phys. 90 (1993) 271-292

Physics

High Energy Physics

High Energy Physics - Theory

29 pages

Scientific paper

10.1143/PTP.90.271

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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