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A family of inequivalent Weyl representations of canonical commutation relations with applications to quantum field theory
| Title: | A family of inequivalent Weyl representations of canonical commutation relations with applications to quantum field theory |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Keywords: | Boson Fock space | | canonical commutation relations | | inequivalent representation | | quantum field | | time-zero field | | inequivalent representation | | Weyl representation |
| Issue Date: | May-2016 |
| Publisher: | World Scientific |
| Journal Title: | Reviews in Mathematical Physics |
| Volume: | 28 |
| Issue: | 4 |
| Start Page: | 1650007 |
| Publisher DOI: | 10.1142/S0129055X16500070 |
| Abstract: | We consider a family of irreducible Weyl representations of canonical commutation relations with infinite degrees of freedom on the abstract boson Fock space over a complex Hilbert space. Theorems on equivalence or inequivalence of the representations are established. As a simple application of one of these theorems, the well-known inequivalence of the time-zero field and conjugate momentum for different masses in a quantum scalar field theory is rederived with space dimension d >= 1 arbitrary. Also a generalization of representations of the time-zero field and conjugate momentum is presented. Comparison is made with a quantum scalar field in a bounded region in R-d. It is shown that, in the case of a bounded space region with d = 1, 2, 3, the representations for different masses turn out to be mutually equivalent. |
| Rights: | Electronic version of an article published as Rev. Math. Phys., 28, 1650007 (2016) DOI:10.1142/S0129055X16500070 Copyright© 2016 World Scientific Publishing Co. http://www.worldscientific.com/worldscinet/rmp |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/65804 |
| 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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