## Landau and Lifshitz: Course of Theoretical Physics: reviews

The 'Course of Theoretical Physics' by Lev Landau and Evgenii Lifshitz was intended as a nine volume work but ended up as a ten volume work. The ten volumes are:

The dates we have given for each volume is the date of the first publication of the first English edition. All ten volumes have Evgenii Lifshitz as a co-author. Lev Landau and Evgenii Lifshitz are the co-authors of volumes 1-3, 5-8. Volume 4 has Evgenii Lifshitz, Lev Pitaevskii and Vladimir Berestetskii as co-authors. Volumes 9-10 have Evgenii Lifshitz and Lev Pitaevskii as co-authors. We give below extracts from reviews of these volumes. Certain volumes went through many editions and the reviews we quote from reflect some of these later editions as well as the first editions.

**Volume 1:***Mechanics.*(1960).**Volume 2:***The Classical Theory of Fields*. (1951).**Volume 3:***Quantum Mechanics: Non-Relativistic Theory.*(1958).**Volume 4:***Relativistic Quantum Theory*. (1971).**Volume 5:***Statistical Physics*. (1951).**Volume 6:***Fluid Mechanics*. (1959).**Volume 7:***Theory of Elasticity*. (1959).**Volume 8:***Electrodynamics of Continuous Media*. (1960).**Volume 9:***Statistical Physics, Part 2*. (1980).**Volume 10:***Physical Kinetics*. (1981).The dates we have given for each volume is the date of the first publication of the first English edition. All ten volumes have Evgenii Lifshitz as a co-author. Lev Landau and Evgenii Lifshitz are the co-authors of volumes 1-3, 5-8. Volume 4 has Evgenii Lifshitz, Lev Pitaevskii and Vladimir Berestetskii as co-authors. Volumes 9-10 have Evgenii Lifshitz and Lev Pitaevskii as co-authors. We give below extracts from reviews of these volumes. Certain volumes went through many editions and the reviews we quote from reflect some of these later editions as well as the first editions.

**Volume 1:**

*Mechanics.*(1960).

**Review by: Walter S McAfee.**

*American Scientist*

**50**(1) Frontiers of Zealous Research (March 1962), 109A-110A.

This book is volume one of the nine-volume 'Course of Theoretical Physics' written by the same authors. The subject matter is concerned solely with the dynamics of particles and of rigid bodies and the method of development is deductive. The presentation is based throughout on two general principles, namely on Galileo's relativity principle and on Hamilton's principle of least action. ... The authors and translators are to be congratulated for providing a beautifully clear and succinct presentation of Newtonian dynamics essentially as it was developed by Euler, Lagrange, Hamilton, and Jacobi. The method of development of material and the choice of examples make this book extremely useful as a source of techniques in classical mechanics which find application in modern quantum physics.

**Volume 2:**

*The Classical Theory of Fields*. (1951).

**Review by: Edward Lee Hill.**

*Mathematical Reviews*, MR0143451 (26 #1007).

The present edition has been expanded by about 50 pages, mostly by extension of the discussion of the general theory of relativity. The scope and pedagogical intent of the book are substantially unchanged from the first edition. The first English edition appears to have been reasonably successful as a text for advanced courses in theoretical physics, and the revised edition should continue to serve the same role. The authors summarize in neat and compact form those features of the classical theory of the electromagnetic field and the general theory of relativity which theoretical physicists are expected to know. The level of sophistication is determined by the fact that the book starts with a discussion of the special theory of relativity, while the derivations of the equations of motion and the field equations are based on variational principles, most of the derivations being purely formal. The reader who is seeking a mathematically rigorous treatment, or a deeper study of the logical and philosophical foundations of these theories, will not find them here.

**Volume 3:**

*Quantum Mechanics: Non-Relativistic Theory.*(1958).

**Review by: George H Weiss.**

*Science, New Series*

**128**(3327) (1958), 767-768.

This volume is the second to appear in a projected series of nine volumes on theoretical physics by these authors. It is in many ways an excellent introduction to the ideas and the applications to atomic phenomena of non-relativistic quantum mechanics. The strong point of this text is the completeness with which it treats atomic problems. There is an almost exhaustive discussion of angular momentum and spin on an elementary level. Of particular interest are the detailed computations of matrix elements for angular momentum problems and the introduction and use of spinors in the discussion. ... It is difficult to show restraint in praising the chapters on elementary many-body systems. ... this book is an excellent reference for those interested in atomic physics but requires a good deal of supplementary material if used in an introductory course in quantum mechanics.

**Review by: Alfred Weinmann.**

*The Mathematical Gazette*

**43**(346) (1959), 305-306.

'Quantum mechanics' is the third volume of a series on theoretical physics by Landau and Lifshitz. By restricting the book to 'Non-Relativistic theory', the authors exclude all phenomena which "significantly depend on the velocity of light". This results in the absence - most strange in a book which claims to display the physical significance of the theory - of any reference to the emission or absorption of light by an atomic system, Bohr's frequency condition, and selection and intensity rules; surely one of the most important parts of quantum mechanics. Presumably these topics will be discussed in the volume on relativistic quantum theory. ... It is clear that this tremendous amount of material can only be covered in a book of this size, by the utmost brevity of presentation, and the omission of irrelevancies. It is unfortunate that some of the most interesting chapters have suffered most in the process. ... It is not easy to see for whom this book was written. Its usefulness would have been greatly enhanced by a more complete system of references, to fill the almost inevitable gaps in a book of this nature; and also perhaps, by a more thorough treatment of fewer topics. As it stands, many arguments appear rather mysterious, merely through lack of a little explanation. A beginner is likely to find it very difficult, and the presentation is unlikely to appeal to the reader who likes a deductive account of the theory. The large number of topics covered, should make it useful as a basis for preparing a course of lectures, or perhaps for reference.

**Volume 4:**

*Relativistic Quantum Theory*. (1971).

**Review by: Roman Jackiw.**

*American Scientist*

**65**(3) ( 1977), 358.

Landau and Lifshitz's multivolume series of texts on theoretical physics is justly acclaimed, especially for the unique, physically incisive presentation of the material. The Russian mode of education and research in physics, particularly as practiced by Landau's school, is subtly different from the American-western European approach, and the books benefit from the fresh viewpoint. This volume was written after Landau's death and unfortunately does not share with its predecessors these unique qualities. Not that there is anything wrong with the presentation - conventional topics of quantum field theory are adequately treated - but there is no personal imprint on the material. ... The book is one of many that can be recommended to those interested in older results of quantum field theory - the reasonable price makes it especially attractive - but the reader will have to turn elsewhere to learn about contemporary research and results.

**Review by: Jonatham Sapristein.**

*American Scientist*

**71**(3) (1983), 305.

This book, the fourth volume of the Landau and Lifshitz 'Course of Theoretical Physics', stands out by virtue of its treatment of a very large number of special topics in quantum electrodynamics. For example, while a basic treatment of the Dirac equation will discuss its solution for spherically symmetric potentials, ending with the bound-state solutions to the Coulomb problem, this book goes on to give the scattering states in a Coulomb potential, a treatment of ultra-relativistic scattering, the solution to the Dirac equation in an external electromagnetic plane wave, and more. The discussion of radiation from atoms compares in thoroughness with Bethe and Salpeter's book. Other specialized topics not often encountered in textbook form are a detailed treatment of ionization losses of fast particles, the method of equivalent photons, and Sudakov form factors. A particularly outstanding discussion is given of the Euler-Heisenberg effective Lagrangian and photon splitting in a magnetic field. ... the great wealth of applications of quantum electrodynamics given in this book should make it a valuable asset for people interested in field theory.

**Review by: Krzysztof Wódkiewicz.**

*Mathematical Reviews*, MR0602331 (82g:81001).

The first and second parts of the 'Relativistic quantum theory' of the famous Landau-Lifshitz course in theoretical physics have been published, respectively, in 1968 and 1971. ... As a result of the spectacular progress in elementary particle physics over the last years most of the chapters included in the 1971 volume of the 'Relativistic quantum theory' have lost their timeliness. Because of this the authors decided to publish in 1980 a new book under a new title 'Quantum electrodynamics' which is a compilation of the sections on electromagnetic interactions from the two volumes of the first edition. This book covers all topics of quantum electrodynamics included in the first edition with some additional paragraphs related mostly to bremsstrahlung radiation. Such topics as photon splitting in a magnetic field or asymptotic properties of scattering amplitudes have now been included in this book.

**Volume 5:**

*Statistical Physics*. (1951).

**Review by: Alexander L Fetter.**

*American Scientist*

**69**(1) (1981), 88.

This book is the first part of a revised and extended two-part version of the well-known Landau and Lifshitz Statistical Physics, second edition. Since the second part is not yet available in English translation, it is a little difficult to evaluate the overall success of the third edition. The most obvious feature of the new Part 1 is its close similarity to the whole of the previous second edition. Most sections and many chapters are merely reset without evident changes, so that either version is indispensable in any serious physicist's library. The principal additions concern the magnetic properties of gases, fluctuations, symmetry of crystals, and critical phenomena, but the alterations seem insufficient inducement for someone with the previous edition to buy this new Part 1.

**Volume 6:**

*Fluid Mechanics*. (1959).

**Review by: William R Schowalter.**

*American Scientist*

**49**(1) (1961), 66A; 68A.

In this sixth volume of the 'Course of Theoretical Physics' the authors state that "... we have tried to develop as fully as possible all matters of physical interest... we discuss neither approximate methods of calculation ... nor empirical theories devoid of physical significance.,, It is obvious that any book of finite size which attempts to cover the whole subject of continuum fluid mechanics will be somewhat uneven in its depth of treatment. Each specialist in fluid mechanics who reads this book will perhaps feel that his own particular field has not been given adequate attention. ... Nevertheless, this book is a remarkable one for several reasons, not the least of which is the fact that two authors, not primarily known for their efforts in classical fluid mechanics, have plunged into this far-flung subject with a result which at its worst is a bit spotty but at its best is a refreshing and thoughtful survey.... The reviewer especially recommends this book for students and research people with some background in fluid mechanics. If they are not disconcerted by omission of much recent work, they will be rewarded with a fresh and stimulating approach to the subject.

**Volume 7:**

*Theory of Elasticity*. (1959).

**Russian edition.**

**Review by: Louis M Milne-Thomson.**

*Mathematical Reviews*,

**MR0065308 (16,412c).**

Elasticity is confined to infinitesimal strain and comprises: 1) Basic equations; 2) Equilibrium of rods and plates; 3) Elastic waves; 4) Heat conduction ... To cover such a vast field the treatment has to be concise. Nevertheless the exposition is a model of clarity. Approximate and empirical methods are not treated and to the authors' credit they never seem to lose sight of the physical background. The book is clearly intended for physicists, but, in spite of the number of worked problems, it is difficult to see to what class of worker the book will appeal. ... As giving an overall picture, it is a magnificent effort.

**English edition.**

**Review by: The Publisher.**

A comprehensive textbook covering not only the ordinary theory of the deformation of solids, but also some topics not usually found in textbooks on the subject, such as thermal conduction and viscosity in solids, and some problems concerning elastic plates and shells.

**Volume 8:**

*Electrodynamics of Continuous Media*. (1960).

**Russian edition.**

**Review by: Edward Lee Hill**.

*Mathematical Reviews*, MR0099837 (20 #6274).

The series of texts on theoretical physics by the authors has been announced for publication in English translation in 9 volumes. The present volume, on one of the older fields of physics, promises to be one of the most successful from a pedagogic point of view. The subject matter is that usually known as "macroscopic electrodynamics". However, only about one-half of the volume is devoted to subject matter traditionally put under this title. The authors have drawn on their extensive knowledge of modern physics to introduce new material usually treated in other contexts. Electrostatics of conductors and dielectrics, fields with constant currents, magnetostatics, ferromagnetism, and quasi-stationary fields take up about one-half of the volume. The treatment is traditional, for the most part, the novelty consisting mainly in the selection of material and the careful discussion. Two brief chapters on superconductivity and magnetohydrodynamics will be welcomed by many. Then come three chapters on electromagnetic wave propagation and theoretical optics. The final chapters cover the transmission of fast particles through matter, electromagnetic fluctuation, scattering of electromagnetic waves, and the diffraction of X-rays in crystals. The treatment is nowhere very deep, from the point of view of the expert, but it will provide the student with a good summary of the part of the subject which can be rationalized in the form of self-contained mathematical problems. It will appeal to the mathematical reader who wishes to know something of how theoretical physicists think, but who does not really care whether the phenomena referred to exist in actual fact. Quite a number of examples, in the form of problems with solutions, appear throughout the text. No problems for solution by the student are given. This deviation from current practice in American and English texts may lead to some difficulty in class room use, unless problems are included in the translated edition.

**First English edition.**

**Review by: Howard Chang.**

*American Scientist*

**49**(4) (1961), 408A; 410A.

This remarkable textbook is the latest translation of a nine-volume series on theoretical physics by one of the world's foremost and versatile physicists, Lev Landau, and his collaborator, E M Lifshitz. Except for Volume 9, Physical Kinetics, all volumes of this series are now available in English, and their existence should exert considerable influence on the content of graduate courses in theoretical physics in English speaking countries because of their in comparable excellence, incredibly broad scope and up-to-date nature.... As in all previous volumes of this series, numerous interesting and important problems are worked out most ingeniously, albeit rather briefly, making these books so valuable. The book is remarkably free of misprints and the translation is felicitous.

**Second English edition.**

**Review by: Editors of Mathematical Reviews.**

*Mathematical Reviews*, MR0820721 (87a:00001).

The original selection of topics for this volume (in the 1950s) was made so that the material would not become obsolescent; consequently that material is reproduced here with only minor improvements. But a substantial amount of new material had to be provided for the new edition, dealing in particular with magnetic properties of matter and the theory of optical phenomena; new chapters on spatial dispersion and nonlinear optics were added. The chapter on electromagnetic fluctuations was removed from Volume VIII and is now treated, in a different form, in Volume IX.

**Volume 9:**

*Statistical Physics, Part 2*. (1980).

**Review by: Editors of Mathematical Reviews**.

*Mathematical Reviews*, MR0518458 (80d:82002).

This is the ninth volume of the famous series entitled 'A course of theoretical physics'. Volumes I-VIII are co-authored by Landau and Lifshitz. L D Landau's name is absent in the heading of this volume but the authors acknowledge his influence, and claim that his point of view is imprinted in this volume as much as in the previous eight volumes, which he co-authored. Volume V of this series is regarded as part I of a course in statistical mechanics, and Volume IX (under review here) as part II. Landau's theory of quantum fluids, arising from his research on liquid helium isotopes, is the starting point for an investigation of quantum effects in macroscopic bodies. The study of Fermi fluids leads to modelling of properties of metals. The authors comment in the foreword that the properties of superconductivity in metals can be studied directly using this approach without the need of first studying the simpler model of Bose fluids.

**Volume 10:**

*Physical Kinetics*. (1981).

**Review by: Ira B Bernstein.**

*American Scientist*

**71**(2) (1983), 191.

This final volume in the celebrated Landau and Lifshitz series lives up to the standards of its predecessors. In cogent and incisive fashion, it presents not only the classical kinetic theory of gases of Boltzmann and Chapman and Enskog but much of the theory of plasmas. Also touched on are topics such as quantum liquids, metals, superconductors, and phase transitions. The presentation emphasizes the most significant aspects of the theory and will serve admirably the beginning graduate student, who might be put off by more traditional treatments which emphasize the formidable computational details.

**Review by: Mircea Draganu.**

*Mathematical Reviews*, MR0561907 (81h:82001).

This is the closing volume of a series of ten volumes, which actually represent a general course of theoretical physics as was planned by L. D. Landau and the first author more than thirty years ago. ... The aim of this course was to give an up-to-date account of the basic topics of theoretical physics, exhibiting as clearly as possible every theoretical construction. The very theoretical applications, as well as the topics considered by the authors as requiring extended expositions of experimental results (as, for example-from the authors' point of view-the greater part of nuclear physics) were not included. The usefulness and the success of this course have been proved by the great number of successive editions in Russian, English, French, German and other languages. ... In the volume, Physical kinetics, under review, the authors include the microscopic theory of processes in non-equilibrium statistical systems, analyzed either by classical or by quantum methods according to the nature of the problems discussed. However, the mathematical formalism is not presented in full detail; this may have the advantage that the reader's attention is not distracted from the fundamental problems. ... This book succeeds in being an excellent introductory guide to the theory of non-equilibrium processes in statistical systems.

Although not part of the 'Course of Theoretical Physics', we also give a review of another book by Lev Landau and Evgenii Lifshitz, namely

*General Physics*. In fact the edition reviewed is one produced after Lev Landau died and Aleksander Ilyich I Akhiezer (1911-2000) was brought in as a third author.*General Physics. Mechanics and Molecular Physics*, by L D Landau, A I Akhiezer, and E M Lifshitz. (1967).

**Review by: Milton A Rothman.**

*Science, New Series*

**160**(3828) (1968), 667.

This is a book on a very elementary college level, and is not to be confused with the fabulous nine-volume Landau and Lifshitz ''Course of Theoretical Physics''. The first hundred pages cover just enough classical mechanics to lay down the general principles and concepts used in the remainder of the book, which is devoted to elementary kinetic theory, thermodynamics, surface phenomena in liquids, viscosity, the theory of symmetry in crystals, and the kinetics of chemical reactions. In short, this is more of a physical chemistry text than the traditional physics course one might expect from the title General Physics. The history of the book is rather unusual, since it was first written in 1937 but was not published until a few years ago. Rewritten and brought up-to-date by Akhiezer and Lifshitz, it retains some of the old-fashioned style and point of view of the '30's. ... the aim of the authors, as described in the preface, was simply to present the material in the most compact way, and in this they have succeeded very well. The chapter on symmetries in crystals is a small masterpiece, and the qualitative material on phase transitions is handled beautifully. There is an index, but no problems, so this book may not be useful as a classroom text; but it can be highly recommended for supplementary reading or review purposes.