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Symmetry plays an essential role in science - not only in crystallography and quantum theory, where its role has long been explicitly recognized, but also in condensed-matter physics, thermodynamics, chemistry, biology, and others. This text discusses the concept of symmetry and its application to many areas of science. While it includes a detailed introduction to the theory of groups, which forms the mathematical apparatus for describing symmetries, it also includes a much more general discussion of the nature of symmetry and its role in science. Many problems serve to sharpen the reader's understanding, and an extensive bibliography concludes the book.
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Symmetry in Science
Joe Rosen
SYlDlDetry in Science An Introduction to the General Theory With 84 Illustrations
Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest
Joseph Rosen Department of Physics and Astronomy University of Central Arkansas Conway, AR 72035 USA and School of Physics and Astronomy Tel-Aviv University 69978 Tel-Aviv Israel
Library of Congress Cataloging-in-Publication Data Rosen, Joseph, 1933Symmetry in science: an introduction to the general theory / Joseph Rosen. p. ern. Includes bibliographical references and index. ISBN-13: 978-0-387-40629-9 e-ISBN-13: 978-1-4612-2506-5 DOl: 10.1007/978-1-4612-2506-5 1. Symmetry. 2. Group theory. QI72.5.S95R673 1995 501'.51164-dc20
I. Title.
94-30622
Printed on acid-free paper.
© 1995 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 15t edition 1995 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identifieli, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production coordinated by Brian Howe and managed by Natalie Johnson; manufacturing supervised by Jacqui Ashri. Typeset by Asco Trade Typesetting Ltd., Hong Kong.
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For Mira
Preface
This book is a revision and expansion of my book A Symmetry Primer for Scientists, published by Wiley in 1983. I expanded and revised that book mainly because, since it was published, my further questfor symmetry comprehension has led to a deeper understanding of the concepts and ideas underlying and supporting the formal theory of symmetry and its manifestation and application in science that was the main import of A Symmetry Primer for Scientists. Furthermore, during that period some of my ideas about symmetry in science have changed somewhat. So the expansion of the previous book was primarily by the addition of three new chapters of conceptual considerations at the end of the book. That allows the reader to choose an "application" track, whereby he or she leaves the conceptual chapters for the end, or skips them altogether, or to choose a "concept" track, in which the conceptual chapters are read before any formalism or mathematics is approached. The revision involved appending a summary of the six symmetry principles derived in the book, adding a summary section for each chapter, updating the Bibliography, and making various and numerous modifications and additions throughout. As was its predecessor, this book is intended to fill a huge gap