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Gauge theory on a non-simply connected domain and representations of canonical commutation relations
| Title: | Gauge theory on a non-simply connected domain and representations of canonical commutation relations |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Keywords: | gauge invariance | | commutation relations | | hilbert space | | quantum operators | | schroedinger picture | | position operators | | linear momentum operators | | observables |
| Issue Date: | Jun-1995 |
| Publisher: | American Institute of Physics |
| Journal Title: | Journal of Mathematical Physics |
| Volume: | 36 |
| Issue: | 6 |
| Start Page: | 2569 |
| End Page: | 2580 |
| Publisher DOI: | 10.1063/1.531051 |
| Abstract: | A quantum system of a particle interacting with a (non-Abelian) gauge field on the non-simply connected domain M=R^2\{an}<sup>N</sup><sub>n=1</sub> is considered, where an, n=1,...,N, are fixed isolated points in R^2. The gauge potential A of the gauge field is a p×p anti-Hermitian matrix-valued 1-form on M, and may be strongly singular at the points an, n=1,...,N. If A is flat, then the physical momentum and the position operators {Pj,qj}<sup>2</sup><sub>j=1</sub> of the particle satisfy the canonical commutation relations (CCR) with two degrees of freedom on a suitable dense domain of the Hilbert space L^2(R^2;C^p). A necessary and sufficient condition for this representation to be the Schrödinger 2-system is given in terms of the Wilson loops of the rectangles not intersecting an, n=1,...,N. This also gives a characterization for the representation to be non-Schrödinger. It is proven that, for a class of gauge potentials, which is not necessarily flat, Pj is essentially self-adjoint. Moreover, an example, which gives a class of non-Schrödinger representations of the CCR with two degrees of freedom, is discussed in some detail. |
| Rights: | Copyright © 1995 American Institute of Physics |
| Relation: | http://www.aip.org/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/13684 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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