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

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 the Prefaces to English editions of these volumes. Some of the Prefaces are from the first English edition while others are from later editions. |

**Volume 1:**

*Mechanics.*(1960).

The first volume of the 'Course of Theoretical Physics' is naturally devoted to the foundation of the subject, namely classical Newtonian mechanics.

As with the other branches of theoretical physics, our exposition makes no use of the historical approach. From the very beginning it is based on the most general principles: Galileo's principle of relativity, and Hamilton's principle of least action. Only with this approach, indeed, can the exposition form a logical whole and avoid tautological definitions of the fundamental mechanical quantities. It is, moreover, essentially simpler, and leads to the most complete and direct means of solving problems in mechanics. ...

L D Landau

E M Lifshitz

Moscow

November 1959

**Volume 2:**

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

This book is devoted to the presentation of the theory of the electromagnetic and gravitational fields. In accordance with the general plan of our 'Course of Theoretical Physics', we exclude from this volume problems of the electrodynamics of continuous media, and restrict the exposition to "microscopic electrodynamics", the electrodynamics of the vacuum and of point charges.

A complete, logically connected theory of the electromagnetic field includes the special theory of relativity, so the latter has been taken as the basis of the presentation. as the starting point of the derivation of the fundamental equations we take the variational principles, which makes possible the achievement of maximum generality, unity and simplicity of presentation.

The last three chapters are devoted to the presentation of the theory of gravitational fields, i.e. the general theory of relativity. The reader is not assumed to have any previous knowledge of tensor analysis, which is presented in parallel with the development of the theory.

The present edition has been extensively revised from the first English edition, which appeared in 1951. ...

L D Landau

E M Lifshitz

Moscow

September 1961

**Volume 3:**

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

The present book is one of the series on 'Theoretical Physics', in which we endeavour to give an up-to-date account of various departments of that science. the complete series will contain the following nine volumes:** **

1. *Mechanics. *2. *The Classical Theory of Fields*. 3. *Quantum Mechanics: Non-Relativistic Theory.* 4. *Relativistic Quantum Theory*. 5. *Statistical Physics*. 6. *Fluid Mechanics*. 7. *Theory of Elasticity*. 8. * Electrodynamics of Continuous Media*. 9.* Physical Kinetics*.

Of these, volumes 4 and 9 remain to be written.

The scope of modern theoretical physics is very wide, and we have, of course, made no attempt to discuss in these books all that is now included in the subject. One of the principles which guided our choice of material was not to deal with those topics which could not properly be expounded without at the same time giving a detailed account of the existing experimental results. For this reason the greater part of nuclear physics, for example, lies outside the scope of these books. Another principle of selection was not to discuss very complicated applications of the theory. both these criteria are, of course, to some extent subjective.

We have tried to deal as fully as possible with those topics that are included. For this reason we do not, as a rule, give references to the original papers, but simply name their authors. We give bibliographical references only to work which contains matters not fully expounded by us, which by their complexity lie "on the borderline" as regards selection or rejection. We have tried also to indicate sources of material which might be of use for reference. even with these limitations, however, the bibliography given makes no pretence of being exhaustive.

We attempt to discuss general topics in such a way that the physical significance of the theory is exhibited as clearly as possible, and then to build up the mathematical formalism. In doing so, we do not aim at "mathematical rigour" of exposition, which in theoretical physics often amounts to self-deception.

The present volume is devoted to non-relativistic quantum mechanics. By "relativistic theory" we here mean, in the widest sense, the theory of all quantum phenomena which significantly depend on the velocity of light. The volume on this subject (volume 4) will therefore contain not only Dirac's relativistic theory and what is now known as quantum electrodynamics, but also the whole of the quantum theory of radiation.

L D Landau

E M Lifshitz

Institute of Physical Problems

USSR Academy of Sciences

August 1956

**Volume 4:**

*Relativistic Quantum Theory*. (1971).

In accordance with the general plan of this 'Course of Theoretical Physics', the present volume deals with the relativistic quantum theory in the broad sense: the theory of all phenomena which depend upon the finite velocity of light, including the whole of the theory of radiation.

This branch of theoretical physics is still far from completion, even as regards its basic principles, and this is particularly true of the theory of strong and weak interactions. But even quantum electrodynamics, despite the remarkable achievements of the last twenty years, still lacks a satisfactory logical structure.

In the choice of material for this book we have considered only results which appear to be reasonably firmly established. In consequence, of course, the greater part of the book is devoted to quantum electrodynamics. We have tried to give a realistic exposition, with emphasis on the physical hypotheses used in the theory, but without going into details of justifications, which in the present state of the theory are in any case purely formal.

In the discussion of specific applications of the theory, our aim has been not to include the whole vast range of effects but to select only the most fundamental of them, adding some references to original papers which contain more detailed studies. we have often omitted some of the intermediate steps in the calculations, which in this subject are usually very lengthy, but we have always sought to indicate any non-trivial point of technique.

The discussion in this book demands a higher degree of previous knowledge on the part of the reader than do the other volumes in the 'Course'. Our assumption has been that a reader whose study of theoretical physics has extended as far as the quantum theory of fields has no further need of predigested material.

The division of the book into two parts has no fundamental significance, and is due only to the large amount of matter to be treated. The second part will deal with radiative corrections in electrodynamics, the theory of weak interactions, and certain problems in the theory of strong interactions.

This book has been written without the direct assistance of our teacher, L D Landau. yet we have striven to be guided by the spirit and the approach of theoretical physics which characterised his teaching of us and which is embodied in the other volumes. We have often asked ourselves what would be the attitude of 'Dau to this or that topic, and sought the answer prompted by our many years' association with him.

V B Berestetskii, E M Lifshitz and L P Pitaevskii

June 1967

**Volume 5:**

*Statistical Physics*. (1951).

**First Edition.**

The present volume of the 'Theoretical physics' series is devoted to an exposition of statistical physics and thermodynamics. These two subjects are firmly interconnected, and in our opinion it is rational to present them together as one whole.

As in the other volumes, we have endeavoured, on the one hand, to present their many specific applications as fully as possible. However, the present book does not contain the theory of electric and magnetic properties of matter, which are treated in anther volume which is dealing with the electrodynamics of material media. Similarly, problems of non-equilibrium phenomena are not treated; we propose to consider these in a separate volume.

We have not included in this book the various theories of ordinary liquids and of strong solutions, which to us appear neither convincing nor useful.

We do not share the view, which one encounters sometimes, that statistical physics is the least well-founded branch of theoretical physics (as regards its basic principles). We believe that the difficulties are created artificially, because the problems are often not stated sufficiently rationally. If one talks from the very beginning about the statistical distribution for small parts of a system (subsystems) and not for a closed system as a whole, then one avoids the whole question of the ergodic or similar hypotheses, which are not really essential for physical statistics.

L D Landau

E M Lifshitz

Moscow

**Second edition.**

For this edition the book has been enlarged and the treatment in some places revised. The revision has, however, been incomplete to the extent that the book does not include topics related to the successful application in recent years of the methods of quantum field theory to statistical physics.

The reason for this is that we have always attempted to construct the 'Course of Theoretical Physics' as describing a single science, interlinking the discussion of its various branches in the different volumes. According to the general plan of the 'Course', this volume should have followed the one on quantum field theory, and the discussion of the above mentioned methods in this book should have been based on the development of them in the previous volume. Since the latter has not yet been completed, it was not possible to include these methods in the present edition.

To my profound regret, L D Landau, my teacher and friend, has been prevented by injuries received in a road accident from personally contributing to the preparation of this new edition.

E M Lifshitz

April 1966

The publishers learnt with deep regret of the death of Professor L D Landau in April 1968 while this volume was in press.

**Volume 6:**

*Fluid Mechanics*. (1959).

The present book deals with fluid mechanics, i.e. the theory of the motion of liquids and gases.

The nature of the book is largely determined by the fact that it describes fluid mechanics as a branch of theoretical physics, and is therefore markedly different from other textbooks on the same subject. We have tried to develop as fully as possible all matters of physical interest, and to do so in such a way as to give the clearest possible picture of the phenomena and their interrelation. Accordingly, we discuss neither approximate methods of calculation in fluid mechanics, nor empirical theories devoid of physical significance. On the other hand, accounts are given of some topics not usually found in textbooks on the subject: the theory of heat transfer and diffusion in fluids; acoustics; the theory of combustion; the dynamics of superfluids; and relativistic fluid dynamics.

In a field which has been so extensively studied as fluid mechanics it was inevitable that important new results should have appeared during the several years since the last Russian edition was published. Unfortunately, our preoccupation with other matters has prevented us from including these results in the English edition. We have merely added one further chapter, on the general theory of fluctuations in fluid dynamics.

L D Landau

E M Lifshitz

Moscow

**Volume 7:**

*Theory of Elasticity*. (1959).

**First edition.**

The present volume of our 'Theoretical Physics' deals with the theory of elasticity.

Being written by physicists, and primarily for physicists, it naturally includes 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 various problems in the theory of elastic vibrations and waves. On the other hand, we have discussed only very briefly certain special matters, such as complex mathematical methods in the theory of elasticity and the theory of shells, which are outside the scope of this book.

L D Landau

E M Lifshitz

Moscow

**Second edition.**

As well as minor corrections and additions, a chapter on the macroscopic theory of dislocations has been added to this edition. The chapter has been written jointly by myself and A M Kosevich.

E M Lifshitz

Moscow

**Fourth Russian edition.**

The basic content of this book (Chapters I-III, V) has changed little from the first two editions (1944, 1953), in which the theory of elasticity was, by coincidence, lumped together with hydrodynamics in the form of 'continuum mechanics'. Such constancy is a natural result of the fact that the basic equations and results of the theory of elasticity had long since 'stagnated'. In the third edition (1965), a chapter was added on the theory of dislocations in crystals (written together with Kosevich); this chapter has now undergone comparatively small changes. In the present edition a new chapter has been added that is devoted to the mechanics of liquid crystals; it was written together with Pitaevskii. This new field of continuum mechanics contains, simultaneously, features typical of the mechanics of fluid and elastic media. Therefore it seems appropriate to place its presentation in the present course after the presentations of hydrodynamics and the theory of elasticity of rigid bodies.

**Volume 8:**

*Electrodynamics of Continuous Media*. (1960).

**First Edition.**

The present volume in the 'Course of Theoretical Physics' deals with the theory of electromagnetic properties of matter. These theories include a very wide range of topics ...

In writing this book we have experienced considerable difficulties, partly because of the need to make a selection from the extensive existing material, and partly because the customary exposition of many topics to be included does not possess the necessary physical clarity, and sometimes is actually wrong. We realise that our own treatment still has many defects, which we hope to correct in future editions.

L D Landau

E M Lifshitz

Moscow

June 1959

**Second Edition.**

This second edition is supplemented by a large amount of new material, in particular as regards the theory of magnetic properties of matter and the theory of optical phenomena. There are new chapters on three-dimensional dispersion and on nonlinear optics. The chapter on electromagnetic fluctuation is omitted, since this material is now presented, in altered form, in another volume of this course, Volume IX.

**Volume 9:**

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

As a brief characterisation of its contents, this ninth volume in the 'Course of Theoretical Physics' may be said to deal with the quantum theory of the condensed state of matter. It opens with a detailed exposition of the theory of Bose and Fermi quantum liquids. This theory, set up by L D Landau following the experimental discoveries by P L Kapitza, is now an independent branch of theoretical physics. Its importance is in fact measured not so much by even the remarkable phenomena that occur in the liquid isotopes of helium as by the fact that the concepts of a quantum liquid and its spectrum are essentially the foundation for the quantum description of macroscopic bodies.

For example, a thorough understanding of the properties of metals involves treating the electrons in them as a Fermi liquid. The properties of the electron liquid are, however, complicated by the presence of the crystal lattice, and the study of the simpler case of a homogeneous isotropic liquid is a necessary preliminary step in the construction of the theory. Similarly, superconductivity in metals, which may be regarded as superfluidity of the electron liquid, is difficult to understand clearly without a previous knowledge of the simpler theory of superfluidity in a Bose liquid.

The Green's function approach is an indispensable part of the mathematical formalism of modern statistical physics. This is not only because of the convenience of the calculation of Green's functions by the diagram technique, but particularly because the Green's functions directly determine the spectrum of elementary excitations in the body, and therefore constitute the language that affords the most natural description of the properties of these excitations. In the present volume, therefore, considerable attention is paid to methodological problems in the theory of Green's functions of macroscopic bodies. Although the basic ideas of the method are the same for all systems, the specific form of the diagram technique is different in different cases. It is consequently natural to develop these methods for the isotropic quantum liquids, where the essence of the procedure is seen in its purest form, without the complications arising from spatial inhomogeneity, the presence of more than one kind of particle, and so on.

For similar reasons, the microscopic theory of superconductivity is described with the simple model od an isotropic Fermi gas with weak interaction, disregarding the complications due to the presence of the crystal lattice and the Coulomb interaction.

In respect to the chapters dealing with electrons in the crystal lattice and with the theory of magnetism, we must again stress that this book is part of a course of theoretical physics and in no way attempts to be a textbook of solid state theory. Accordingly, only the most general topics are discussed here, and no reference is made to problems that involve the use of specific experimental results, nor to methods of calculation that have no evident theoretical basis. Moreover, this volume does not include the transport properties of solids, with which we intend to deal in the next and final volume of the 'Course'.

Finally, this book also discusses the theory of electromagnetic fluctuations in material media and the theory of hydrodynamic fluctuations. The former was previously intended in Volume 8 'Electrodynamics of Continuous Media'. Its transfer to the present volume is a consequence of the need to make use of Green's functions, whereby the entire theory can be simplified and made more convenient for application. It is also more reasonable to treat electromagnetic and hydrodynamic fluctuations in the same volume.

This is Volume 9 of the 'Course of Theoretical Physics' (Part 1 of 'Statistical Physics' being Volume 5). The logic of the arrangement is that the topics dealt with here are closely akin also to those in fluid mechanics (Volume 6) and macroscopic electrodynamics (Volume 8).

L D Landau is not among those who have actually written this book. But the reader will quickly observe how often his name occurs in it: a considerable part of the results given here are due to him, alone or with his pupils and colleagues. Our many years' association with him enables us to hope that we have accurately reflected his views on these subjects - while at the same time, of course, having regard to developments in the fifteen years since his work was so tragically terminated.

E M Lifshitz

L P Pitaevskii

April 1977

**Volume 10:**

*Physical Kinetics*. (1981).

This final volume of the 'Course of Theoretical Physics' deals with physical kinetics, in the wide sense of the microscopic theory of processes in systems not in statistical equilibrium.

In contrast to the properties of systems that are in statistical equilibrium, the kinetic properties are much more closely related to the nature of the microscopic interactions in a particular physical object. This is the reason for the enormous variety in such properties and the considerably greater complexity of the relevant theory. The choice of topics to be included in a general course of theoretical physics thereby become less clear.

Much attention is given to the theory of gases, as the simplest branch, in principle, of kinetic theory. Several chapters are concerned with plasma theory, not only because of the intrinsic physical significance of this department of kinetic theory, but also because many of the problems involved can be completely solved and furnish an instructive illustration of the general methods of kinetic theory.

The kinetic properties of solids are especially multifarious. In the selection of material for the chapters in question, we naturally had to confine ourselves to the most general subjects which exhibit the basic physical kinetic phenomena and the methods of treating them. Here we must again emphasis that the book is part of a course of theoretical physics, and does not set out to be a textbook of solid state theory.

There are two evident omissions from the book: the kinetics of magnetic processes, and the theory of transport phenomena arise from the passage of fast particles through matter. Thes omissions are due to lack of time, and we resolved to accept them for the present edition, so as not to delay its publication any further. We trust that, although the book does not contain all that it might, everything in it will be found both interesting and useful.

This volume completes the programme laid down by Lev Davidovich Landau more than forty years ago.

E M Lifshitz

L P Pitaevskii

November 1978

JOC/EFR January 2014

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