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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

書籍の購入

イーブック ¥11,231
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • 予定日: February 4, 2020
  • ISBN 978-981-15-2180-5
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: EPUB, PDF
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
ハードカバー ¥14,039
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • 予定日: February 5, 2020
  • ISBN 978-981-15-2179-9
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
この書籍について

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)

書籍の購入

イーブック ¥11,231
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • 予定日: February 4, 2020
  • ISBN 978-981-15-2180-5
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: EPUB, PDF
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
ハードカバー ¥14,039
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • 予定日: February 5, 2020
  • ISBN 978-981-15-2179-9
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
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書誌情報

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.
イーブック ISBN
978-981-15-2180-5
DOI
10.1007/978-981-15-2180-5
ハードカバー ISBN
978-981-15-2179-9
Series ISSN
0921-3767
Edition Number
1
Number of Pages
XIX, 493
Number of Illustrations
6 b/w illustrations
Topics