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

Buch 19 von 24: Mathematical Physics Studies

Arai, Asao

 
9789811521799: Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations: Representation-theoretical Viewpoint for Quantum Phenomena (Mathematical Physics Studies)
Hardcover
ISBN 10: 9811521794 ISBN 13: 9789811521799
Verlag: Springer, 2020

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

Professor Asao Arai is a Professor Emeritus of Hokkaido University.

Von der hinteren Coverseite

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.

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Verlag
Springer
Erscheinungsdatum
2020
Sprache
Englisch
ISBN 10 
9811521794
ISBN 13 
9789811521799
Einband
Gebundene Ausgabe
Auflage
1
Anzahl der Seiten
512
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