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Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations: Representation-theoretical Viewpoint for Quantum Phenomena (Mathematical Physics Studies) - Softcover

Book 19 of 24: Mathematical Physics Studies

Arai, Asao

 
9789811521829: Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations: Representation-theoretical Viewpoint for Quantum Phenomena (Mathematical Physics Studies)
Softcover
ISBN 10: 9811521824 ISBN 13: 9789811521829
Publisher: Springer, 2021

Synopsis

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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2021
Language
English
ISBN 10 
9811521824
ISBN 13 
9789811521829
Binding
Paperback
Edition number
1
Number of pages
512