Group Representation for Quantum Theory
This book explains the group representation theory for quantum theory in the language of quantum theory. As is well known, group representation theory is very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin
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Group Representation for Quantum Theory
Group Representation for Quantum Theory
Masahito Hayashi
Group Representation for Quantum Theory
123
Masahito Hayashi Graduate School of Mathematics Nagoya University Nagoya Japan
ISBN 978-3-319-44904-3 DOI 10.1007/978-3-319-44906-7
ISBN 978-3-319-44906-7
(eBook)
Library of Congress Control Number: 2016950886 © Springer International Publishing Switzerland 2017 Springer received copyright for English version only. This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book is the English edition of the Japanese book Group Representations for Quantum Theory, which was originally published by Kyoritsu shuppan, Tokyo, Japan in January 2014. The original Japanese book covers several topics in representation theory that is related to quantum theory. As is well known, group representation theory is a very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin–orbit interaction, quark model, quantum optics, and quantum information processing including quantum error correction. Therefore, many departments of physics have lecture courses for mathematics for physics, in particular, they have a graduate lecture course for representation theory for physics. This book conducts lecture courses on mathematics for physicists. When the contents of this book are too much for the lecture course, this book can be used by skipping several detailed parts. To describe a big picture of application of representation theory to quantum theory, the book needs to contain the following six topics, permutation group, SU(2) and SUðdÞ, Heisenberg representation, squeezing operation, Discrete Heisenberg representation, and the relation with Fourier transform from a unified viewpoint by including
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