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

Arai, Asao

Hokkaido University Preprint Series in Mathematics, 2015, 1085, 1-24

Permalink : https://doi.org/10.14943/84229

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DOI	https://doi.org/10.14943/84229
URI	https://hdl.handle.net/2115/69889
タイトル	A Family of Inequivalent Weyl Representations of Canonical Commutation Relations with Applications to Quantum Field Theory
著者	著者名 Arai, Asao
言語	英語
キーワード	Boson Fock space
	canonical commutation relations
	inequivalent representation
	quantum eld
	time-zero eld
	Weyl representation.
発行日	2015-12-18
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1085
ページ	1-24
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record