Quantization on a torus without position operators
نویسنده
چکیده
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 representation of the algebra is unitarily equivalent to each other. This work provides a firm foundation for the noncommutative torus theory. PACS: 02.40.Gh; 03.65.Ca; 03.65.Fd; 04.60.Ds To be published in Modern Physics Letters A. e-mail: [email protected] 1
منابع مشابه
Quantization without position operators
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 ...
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