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 an 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… (More)

@inproceedings{Tanimura2003QuantizationOA,
title={Quantization on a torus without position operators},
author={Shogo Tanimura},
year={2003}
}