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A Family of Inequivalent Weyl Representations of Canonical Commutation Relations with Applications to Quantum Field Theory

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84229

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
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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