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Field name	Details
Dewey Class	530.15
Title	Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations ([EBook]) : Representation-theoretical Viewpoint for Quantum Phenomena / / by Asao Arai.
Author	Arai, Asao
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2020.
Publication	Singapore : : Springer Singapore : : Imprint: Springer, , 2020.
Physical Details	XIX, 493 p. 6 illus. : online resource.
Series	Mathematical physics studies 0921-3767
ISBN	9789811521805
Summary Note	Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory. From a structural viewpoint, quantum physics can be primarily understood as Hilbert space representations of CCR or CAR. There are many interesting physical phenomena which can be more clearly understood from a representation-theoretical viewpoint with CCR or CAR. This book provides an introduction to representation theories of CCR and CAR in view of quantum physics. Particular emphases are put on the importance of inequivalent representations of CCR or CAR, which may be related to characteristic physical phenomena. The topics presented include general theories of representations of CCR and CAR with finite and infinite degrees of freedom, the Aharonov-Bohm effect, time operators, quantum field theories based on Fock spaces, Bogoliubov transformations, and relations of infinite renormalizations with inequivalent representations of CCR. This book can be used as a text for an advanced topics course in mathematical physics or mathematics.:
Contents note	Mathematical Preliminaries -- Representations of Canonical Commutation Relations with Finite -- Aharonov-Bohm Effect and Inequivalent Representations of CCR -- Time Operators -- Representations of Canonical Anti-commutation Relations with Finite Degrees of Freedom -- Elements of the Theory of Boson Fock Spaces -- Elements of the Theory of Fermion Fock Spaces -- Representations of CCR with Infinite Degrees of Freedom -- Representations of CAR with Infinite Degrees of Freedom -- Physical Correspondences in Quantum Field Theory.
Mode of acces to digital resource	Digital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note	- Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-981-15-2180-5
Links to Related Works	Subject References: Functional Analysis . Mathematical Physics . Quantum Physics . Authors: Arai, Asao . author . Corporate Authors: SpringerLink (Online service) . Series: Mathematical physics studies . Classification: 530.15 .

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Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations: Representation-theoretical Viewpoint for Quantum Phenomena

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