Quantization on a torus without position operators
High Energy Physics - Theory
2009-11-10 v2 Quantum Physics
Abstract
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.
Cite
@article{arxiv.hep-th/0309091,
title = {Quantization on a torus without position operators},
author = {Shogo Tanimura},
journal= {arXiv preprint arXiv:hep-th/0309091},
year = {2009}
}
Comments
12 pages, LaTeX2e, the title is changed, minor corrections are made, references are added. To be published in Modern Physics Letters A