Theory of Spinors and Its Application in Physics and Mechanics
This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered.The main mathematical
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Theory of Spinors and Its Application in Physics and Mechanics
Theory of Spinors and Its Application in Physics and Mechanics
Vladimir A. Zhelnorovich
Theory of Spinors and Its Application in Physics and Mechanics
123
Vladimir A. Zhelnorovich Institute of Mechanics Moscow State University Moscow, Russia
ISBN 978-3-030-27835-9 ISBN 978-3-030-27836-6 (eBook) https://doi.org/10.1007/978-3-030-27836-6 This book is a revised and updated version of the original Russian edition “Theory of Spinors and its Application in Physics and Mechanics” published by Izdatel’stvo Nauka, Moscow, Russia, 1982. © Springer Nature Switzerland AG 2019 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book is a reworked and enlarged version of the author’s book [82]. The first chapter of the book presents the theory of spinors in n-dimensional (in general case complex) Euclidean spaces. The second chapter contains an exposition of the theory of spinors in Riemannian spaces. The third and fourth chapters are devoted to the theory of spinors and to the methods of their tensor representation in four- and three-dimensional spaces. Along with the material in the book [82], these chapters contain the results of recent papers, related in particular to the use of proper orthonormal tetrads defined by spinors. Some very useful relations are obtained that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The main content of the fifth chapter is the tensor representation of a wide class of relativistically invariant spinor differential equations that contain, as a particular case, the known spinor equations of field theory. As an example of the application of
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