Mathematical Physics Studies

Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations

Representation-theoretical Viewpoint for Quantum Phenomena

Authors: Arai, Asao

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  • Presents a unified viewpoint for quantum physics, both in quantum mechanics and quantum field theoryClarifies physical meanings of inequivalent  representations of CCR or CARGives representation–theoretical analyses to infinite renormalizations in some quantum field modelsIncludes representation–theoretical characterizations for fundamental quantities such as masses and chargesContains mathematical descriptions in detail throughout the main text

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eBook 28,88 €
71,68 € (listprice)
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  • ISBN 978-981-15-2180-5
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Hardcover 51,99 €
124,79 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-981-15-2179-9
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  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
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Softcover 36,39 €
88,39 € (listprice)
price for Spain (gross)
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  • ISBN 978-981-15-2182-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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About this book

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.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook 28,88 €
71,68 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-981-15-2180-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 51,99 €
124,79 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-981-15-2179-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 36,39 €
88,39 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-981-15-2182-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations
Book Subtitle
Representation-theoretical Viewpoint for Quantum Phenomena
Authors
Series Title
Mathematical Physics Studies
Copyright
2020
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-2180-5
DOI
10.1007/978-981-15-2180-5
Hardcover ISBN
978-981-15-2179-9
Softcover ISBN
978-981-15-2182-9
Series ISSN
0921-3767
Edition Number
1
Number of Pages
XIX, 493
Number of Illustrations
6 b/w illustrations
Topics