Quantization on a torus without position operators
高能物理 - 理论
2009-11-10 v2 量子物理
摘要
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.
引用
@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}
}
备注
12 pages, LaTeX2e, the title is changed, minor corrections are made, references are added. To be published in Modern Physics Letters A