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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 |
Keywords: | Boson Fock space | canonical commutation relations | inequivalent representation | quantum eld | time-zero eld | Weyl representation. |
Issue Date: | 18-Dec-2015 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 1085 |
Start Page: | 1 |
End Page: | 24 |
Abstract: | Considered is a family of irreducible Weyl representations of canonical commu- tation relations with in nite 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 eld and conjugate momentum for different masses in a quantum scalar eld theory is rederived with space dimension d 1 arbitrary. Also a generalization of representations of the time-zero eld and conjugate momentum is presented. Comparison is made with a quantum scalar eld in a bounded region in Rd. 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. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69889 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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