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Construction of a Weyl Representation from a Weak Weyl Representation of the Canonical Commutation Relation

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Abstract

Weak Weyl representations of the canonical commutation relation (CCR) with one degree of freedom are considered in relation to the theory of time operator in quantum mechanics. It is proven that there exists a general structure through which a weak Weyl representation can be constructed from a given weak Weyl representation. As a corollary, it is shown that a Weyl representation of the CCR can be constructed from a weak Weyl representation which satisfies some additional property. Some examples are given.

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Authors and Affiliations

  1. Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

    Asao Arai & Yasumichi Matsuzawa

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  1. Asao Arai
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  2. Yasumichi Matsuzawa
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Correspondence to Asao Arai.

Additional information

The work is supported by the Grant-in-Aid No.17340032 for Scientific Research from Japan Society for the Promotion of Science (JSPS).

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Arai, A., Matsuzawa, Y. Construction of a Weyl Representation from a Weak Weyl Representation of the Canonical Commutation Relation. Lett Math Phys 83, 201–211 (2008). https://doi.org/10.1007/s11005-008-0220-4

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  • DOI: https://doi.org/10.1007/s11005-008-0220-4

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