Quantization on a torus without position operators

Details Quantization on a torus without position operators Quantization on a torus without position operators

2003-09-09

arxiv.org/abs/hep-th/0309091v2

Mod.Phys.Lett. A18 (2003) 2755-2765

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX2e, the title is changed, minor corrections are made, references are added. To be published in Modern Physics L

Scientific paper

10.1142/S0217732303012301

We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct irreducible representation of the algebra. We show that it realizes quantum mechanics of a charged particle in a uniform magnetic field. We prove that any irreducible representation of the algebra is unitary equivalent to each other. This work provides a firm foundation for the noncommutative torus theory.

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