E-Book Overview
Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar-Herbst and Brown-Ravenhall, which are semibounded under appropriate circumstances. This book contains an up-to-date, comprehensive and self-contained analysis of the spectral properties of these operators, providing the tools for anyone working in this area. Another major feature is the work of the authors on zero modes, a topic which has important significance for the stability of matter and other physical problems. Up until now, these topics have been scattered throughout the literature, without a systematic and cohesive treatment. The book will report largely on the progress on these topics published since 1992.
E-Book Content
SPECTRAL ANALYSIS ._
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1RELATIVISTIC RELATIVISTIC OPERATORS A A Balinsky W D Evans
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spectral analysis of
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spectral analysis of
relativistic operators A A Balinsky and W D Evans Cardiff University, UK
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Imperial College Press
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Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.
SPECTRAL ANALYSIS OF RELATIVISTIC OPERATORS Copyright © 2011 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
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ISBN-13 978-1-84816-218-1 ISBN-10 1-84816-218-9
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Preface
The symbiotic relationship between mathematics and physics has seldom been more apparent than in the development of quantum mechanics and the spectral theory of self-adjoint operators in Hilbert spaces since the early years of the last century. The lofty position that quantum mechanics has attained in science has corresponded with the creation of powerful and elegant theories in functional analysis and operator theory, each feeding voraciously on the problems and discoveries of the other. At the core of this activity, the s