A.B. Migdal - Qualitative Methods in Quantum Theory

Qualitative Methods in Quantum Theory

Qualitative Methods in Quantum Theory

A. B. Migdal

I. V. Kurchatov Atomic Energy Institute
Moscow, Russia

Translated from the Russian edition by

Anthony J. Leggett

University of Sussex

First published 1977 by Westview Press

Published 2018 by CRC Press

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ADVANCED BOOK CLASSICS

David Pines, Series Editor

Anderson, P.W., Basic Notions of Condensed Matter Physics

Bethe H. and Jackiw, R., Intermediate Quantum Mechanics, Third Edition

Cowan, G. and Pines, D., Complexity: Metaphors, Models, and Reality

de Gennes, P.G., Superconductivity of Metals and Alloys

dEspagnat, B., Conceptual Foundations of Quantum Mechanics, Second Edition

Feynman, R., Photon-Hadron Interactions

Feynman, R., Quantum Electrodynamics

Feynman, R., Statistical Mechanics

Feynman, R., The Theory of Fundamental Processes

Gell-Mann, M. and Neeman, Y., The Eightfold Way

Khalatnikov, I. M. An Introduction to the Theory of Superfluidity

Ma, S-K., Modern Theory of Critical Phenomena

Migdal, A. B., Qualitative Methods in Quantum Theory

Negele, J. W. and Orland, H., Quantum Many-Particle Systems

Nozires, P., Theory of Interacting Fermi Systems

Nozires, P. and Pines, D., The Theory of Quantum Liquids

Parisi, G., Statistical Field Theory

Pines, D., Elementary Excitations in Solids

Pines, D., The Many-Body Problem

Quigg, C., Gauge Theories of the Strong, Weak, and Electromagnetic Interactions

Schrieffer, J.R., Theory of Superconductivity, Revised

Schwinger, J., Particles, Sources, and Fields, Volume I

Schwinger, J., Particles, Sources, and Fields, Volume II

Schwinger, J., Particles, Sources, and Fields, Volume III

Schwinger, J., Quantum Kinematics and Dynamics

Wyld, H.W., Mathematical Methods for Physics

CONTENTS

Perseus Publishings Frontiers in Physics series has, since 1961, made it possible for leading physicists to communicate in coherent fashion their views of recent developments in the most exciting and active fields of physicswithout having to devote the time and energy required to prepare a formal review or monograph. Indeed, throughout its nearly forty year existence, the series has emphasized informality in both style and content, as well as pedagogical clarity. Over time, it was expected that these informal accounts would be replaced by more formal counterpartstextbooks or monographsas the cutting-edge topics they treated gradually became integrated into the body of physics knowledge and reader interest dwindled. However, this has not proven to be the case for a number of the volumes in the series: Many works have remained in print on an on-demand basis, while others have such intrinsic value that the physics community has urged us to extend their life span.

The Advanced Book Classics series has been designed to meet this demand. It will keep in print those volumes in Frontiers in Physics that continue to provide a unique account of a topic of lasting interest. And through a sizable printing, these classics will be made available at a comparatively modest cost to the reader.

The late Arkady B. Migdal was one of the great theoretical physicists of our time, who made significant contributions to nuclear physics, condensed matter physics, astrophysics, and particle physics. He combined keen physical insight with a deep understanding of physics and physical phenomena and believed it truly important that students learn more about quantum theory than about the mathematical manipulation of formulae and equations. It was for that reason that he developed the series of lectures on qualitative methods in quantum theory that are contained in this book. Migdals originality and careful attention to pedagogy make his book, Qualitative Methods in Quantum Theory, required reading for every scientist interested in learning and applying quantum theory. I am most pleased that its publication in Advanced Book Classics will now make it readily available to the future generation of scientists, who may be expected to profit greatly from reading it.

David Pines

Cambridge, England

May, 2000

In the interests of rapid and economical production most of the equations in this book have been photocopied directly from the Russian version. Generally, notations which may be unfamiliar to English-speaking readers have been changed to conform to the English usage, but there are a few cases where this has proved awkward or impossible; the most frequent ones are the following:

A simple sequence of two vectors (indicated by boldface) denotes the scalar or dot product.

The notation [a, b] with a, b boldface denotes the vector product of a and b.

r2, R2 denotes the Laplacian with respect to r and R respectively.

sh indicates hyperbolic sine. (sinh)

Sp indicates the trace of a matrix.

The solution of most problems in theoretical physics begins with the application of the qualitative methods which constitute the most attractive and beautiful characteristic of this discipline. By qualitative methods we mean dimensional estimates and estimates made by using simple models, the investigation of limiting cases where one can exploit the smallness of some parameter, the use of the analytic properties of physical quantities, and finally the derivation of consequences from the symmetry properties, that is, the invariance relative to various transformations (e.g. Lorentz or isotopic invariance). However, as experience in the classroom shows, it is just these aspects of theoretical physics which are most difficult for the beginner.