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The introduction of quantum field theory methods has led to a kind of “revolution” in condensed matter theory. This resulted in the increased importance of Feynman diagrams or diagram technique. It has now become imperative for professionals in condensed matter theory to have a thorough knowledge of this method. There are many good books that cover the general aspects of diagrammatic methods. At the same time, there has been a rising need for books that describe calculations and methodical “know how” of specific problems for beginners in graduate and postgraduate courses. This unique collection of lectures addresses this need. The aim of these lectures is to demonstrate the application of the diagram technique to different problems of condensed matter theory. Some of these problems are not “finally” solved. But the development of results from any section of this book may serve as a starting point for a serious theoretical study.
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DIVJUMATICJ Lectures on Selected Problems in Condensed Matter Theory
MICHAEL V. SADOVSKU
World Scientific
Di\j[\MM\TI(f Lectures on Selected Problems in Condensed Matter Theory
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Lectures on Selected Problems in Condensed Matter Theory
MICHAEL V. SADOVSKII Russian Academy of Sciences, Russia
YJ? World Scientific NEW JERSEY
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DIAGRAMMATICS Lectures on Selected Problems in Condensed Matter Theory Copyright © 2006 by World Scientific Publishing Co. Pte. Ltd. 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 981-256-639-2
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It is necessary to overcome mysticism with respect to techniques...
Chairman Mao Zedong
Oh? The man works and doesn't tell his assistant what he is doing...? He will never give that seminar.
W. Pauli to R.P. Feynman
\ V
L.P. Gorkov, A.A. Abrikosov, I.E. Dzyaloshinskii, Argonne, USA, 1998
Preface
At the end of 1950s and in early 1960s there was a kind of "revolution" in the theory of condensed matter (at that time called mostly the theory of solid state and quantum liquids) which was due to the use of methods, developed a decade earlier in quantum field theory, mainly the method of Feynman diagrams. Since that time diagrammatic methods became the foundation of this section of theoretical physics, and the knowledge of these is absolutely necessary for any professional working in this field. A number of good books are devoted to rather detailed exposition of the general aspects of these methods, such as the introduction of diagrammatic formalism for different types of interactions [Abrikosov A.A., Gorkov L.P., Dzyaloshinskii I.E. (1963); Lifshits E.M., Pitaevskii L.P. (1980)]. Of course, most of these books contain also discussion of some specific applications of these methods to conc