See discussions, stats, and author profiles for this publication at: https://www.researchgate.

net/publication/368607719

Theorminima. A sufficient minimum of knowledge in Theoretical Physics

Method · February 2023

CITATIONS READS

0 77

1 author:

Alexei M. Frolov
The University of Western Ontario
479 PUBLICATIONS   3,249 CITATIONS   

SEE PROFILE

Some of the authors of this publication are also working on these related projects:

project 1 View project

All content following this page was uploaded by Alexei M. Frolov on 27 May 2023.

The user has requested enhancement of the downloaded file.

 Theorminima.
A sufficient minimum of knowledge in Theoretical Physics

by Alexei M Frolov

Department of Applied Mathematics,

University of Western Ontario, London, Ontario N6H 5B7, Canada
23rd of February 2023

(DOI: 10.13140/RG.2.2.23017.77928)

Here I want to talk about theoretical minimum, or minimal knowledge in theoretical

physics, which is sufficient for successful and independent work in this area. Such a theo-
retical minimum usually means an elementary combination of a few directions (or areas) in
Theoretical Physics. There were quite a few well known research groups around the World
where without passing a certain minimum in physics (and sometimes in mathematics too)
the candidate cannot continue to work. The most famous such a group in theoretical physics
was Lev Landau’s group at the Institute for Physical Problems in Moscow. In reality, the
well known course of theoretical physics (currently in 10 volumes) by L.D. Landau and E.M.
Lifshitz was originally planned as a series of textbooks for PhD students and co-workers
which were passing seven exams (plus two in math) in order to obtain some “necessary and
sufficient” minimum in theoretical physics. For example, in the preface to the second edition
of the fifth volume of this course (‘Statistical Physics’) in Russian one finds recommenda-
tions about what sections of the book can be skipped without any prejudice of passing the
“Minimum”.
However, the main goal of preparing for the theoretical minimum is not to pass the next
exam (or even several exams), but to master the subject itself. Additional fundamental
knowledge always gives you a real freedom. The freedom to choose a new direction for

1
your research and teaching, the freedom to read and understand literature, the freedom to
communicate freely with friends and colleagues at various conferences, lectures, meetings,
seminars, etc. Finally, based on the old Landau’s approach I have developed a similar
approach which can be used by everyone who wants to become a productive and prominent
physicist in the future. There are only a very few conditions for this. In particular, you must
have a strong will and a good memory in order to complete such a self-education project in
theoretical physics. Also, it is better to start the program in the ‘golden’ age, i.e., when you
are between 23 and 27 years old. However, it did work for a number of older people too.
The whole course usually takes approximately between 7 and 10 years, if you are busy
with work, teaching, business, etc. However, if you are a PhD student and have an additional
time to study, then you can finish it in 5 - 5.5 years. It should be no rush here! The method
proposed below is based on an intense and continuous reading of a number of books for each
selected chapter of theoretical physics (see below). Each book recommended below should
be read, absolutely understood and the logic of the authors’ reasoning well assimilated.
All examples and problems offered in each book should be solved (if possible in several
ways). Also, I have to emphasize that it is crucially important to read a number of different
books on each Chapter of Theoretical Physics. Only by using this approach you can get
a complete picture of the subject being studied, and not become a fan of some author(s)
and unconditionally accept his/their views (often erroneous and incomplete) on this area of
physics.
How to understand that our approach works for you? A simple criterion does exist: just
take a picture of your face every six months. New picture should look smarter than the
previous one. If this is the case, then you are on a right truck. After you have finished
this program, then you became an expert in theoretical physics. Now, you can easily pass
any formal exams for ‘theoretical minima’ required in some research groups. Plus, you can
easily read and rapidly understand new research papers in modern journals, teach any of
these and related courses, etc. So, I wish you Good Luck!

Now, let us discuss our method in detail. Currently, there are seven main directions
in Physics and three similar areas of Mathematics which you need to know much deeper
than modern University education can provide even at the MSc and PhD levels. Finally,
based on my personal choices and experience I have chosen the following seven (basic) areas

2
of Theoretical Physics:

1. Classical Mechanics
2. Classical Electrodynamics, Electrodynamics of Continuous Media and Magnetohydrody-
namics
3. Quantum Mechanics. Non-relativistic Theory
4. Quantum Electrodynamics and Relativistic Quantum Mechanics
5. Statistical Physics, Thermodynamics and Physical Kinetics
6. Hydrodynamics and Theory of Elasticity
7. Theory of Group Representations and its Applications in Physics

The three basic areas in Mathematics are:

1. Vector and Tensor Calculus
2. Complex Analysis and Analytical Function
3. Calculus of Variations

The list of recommended books for each area is presented below:

Classical Mechanics. Recommended books:
1). H. Goldstein, Classical Mechanics, (Addison-Wesley Longman, Inc., Cambridge. MA
(1950)). Here I recommend everyone to use only the first edition of this book, which was
written by the author himself.
2). F.R. Gantmakher, Lectures on Analytical Mechanics, (Nauka (Science), Moscow,
(1966)). Probably, this book is the best course on Hamilton methods in classical mechanics.
3). L.D. Landau and E.M. Lifshitz, Mechanics. Course of Theoretical Physics. Volume 1,
3rd revised and enlarged English ed., (Elsevier Science Ltd., Oxford, UK (2000)).
4). C. Lanczos, The Variational Principles of Mechanics, (University of Toronto Press,
Toronto (1970)). Dover’s reprinted copy is also good.

Suggested additional reading on Classical Mechanics. Recommended books:

V.I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed., (Nauka, Moscow,
(1979)).

3
Classical Electrodynamics, Electrodynamics of Continuous Media and Magne-
tohydrodynamics. Recommended books:
1). J.D. Jackson, Classical Electrodynamics, 2nd ed., (John Wiley and Sons, N.Y. (1975)).
In the next editions of this book the important Section 10 is missing.
2). L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields. Course of Theoretical
Physics. Volume 2, 4th English ed. with corrections, (Elsevier Science Ltd., Oxford, UK
(1994)).
3). A.O. Barut, Electrodynamics and Classical Theory of Fields and Particles, 2nd revised
ed., (Dover Publishing Inc., Mineola, N.Y. (1980))
4). L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media. Course of
Theoretical Physics. Volume 8, 2nd revised and enlarged English ed., (Pergamon Press
Ltd., Oxford, UK (1984))
5). M. Born and E. Wolf, Principles of Optics, 6th revised ed., (Pergamon Press Ltd.,
Oxford, UK (1986))

Suggested additional reading on Electrodynamics. Recommended books:

1). A.A. Sokolov and I.M. Ternov, Radiation from Relativistic Electrons, (American Inst.
of Physics, (1986)).

Quantum Mechanics. Non-relativistic Theory. Recommended books:

1). P.A.M. Dirac, The Principles of Quantum Mechanics, 4th revised ed., (Clarendon Press,
Oxford, UK (1999)).
2). L.D. Landau and E.M. Lifshitz, Quantum Mechanics. Non-Relativistic Theory. Course
of Theoretical Physics. Volume 3, 3rd revised and enlarged English ed., (Pergamon Press
Ltd., Oxford, UK (1984)).
3). A.S. Davydov, Quantum Mechanics, 2nd English ed., (Pergamon Press, Oxford, UK
(1965)).
4). L.I. Shiff, Quantum Mechanics, 2nd edition (McGraw-Hill Book Comp., Inc., N.Y.
(1955)).
5). F.A. Kaempffer, Concepts in Quantum Mechanics, (Academic Press, N.Y. (1965)).

Suggested additional reading on Quantum Mechanics. Recommended books:

4
1). H.S. Green, Matrix Mechanics (P. Noordhoff Ltd., Groningen, Netherlands (1965)).
2). H.A. Bethe, Intermediate Quantum Mechanics (W.A. Benjamin, Inc., New York
(1964)).
3). V.A. Fock, Foundations of Quantum Mechanics, (Nauka (Science), Moscow (1976)).
4). P.V. Elutin and V.D. Krivchenkov, Quantum Mechanics with Problems, (Nauka,
Moscow (1976)).
5). J.M. Ziman, Elements of Advanced Quantum Theory (Cambridge Univ. Press,
Cambridge, UK (1995)).

Quantum Electrodynamics and Relativistic Quantum Mechanics. Recommended

books:
1). W. Heitler, Quantum Theory of Radiation, 3rd ed., (Clarendon Press, Oxford, UK
(1954)).
2). A. Akhiezer and V.B. Berestetskii, Quantum Electrodynamics (Interscience, New York,
1965).
3). V.B. Berestetskii, E.M. Lifshitz and L.P. Pitaevskii, Quantum Electrodynamics. Course
of Theoretical Physics. Volume 4, 3rd corrected ed., (Nauka (Science), Moscow, 1989).
4). C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
5). W. Greiner and J. Reinhardt, Quantum Electrodynamics (4th ed., Springer Verlag,
Berlin, 2009).
6). J.D. Bjorken and S.D. Drell, Relativistic Quantum Mechanics and Relativistic Quantum
Fields (McGraw-Hill, New York, 1964).

Suggested additional reading on Quantum Electrodynamics and Relativistic Quan-

tum Mechanics. Recommended books:
1). R. Loudon, Quantum Theory of Light, 3rd ed., (Clarendon Press, Oxford, UK (2000)).
2). F. Mandl and G. Show, Quantum Field Theory, 2nd ed., (John Wiley and Sons, Ltd.
(2010)).

Statistical Physics, Thermodynamics and Physical Kinetics. Recommended books:

1). J.E. Mayer and M. Goeppert Mayer, Statistical Mechanics, 2nd ed., (John Wiley &
Sons, Inc., New York (1977)).

5
2). Yu.B. Rumer and M.Sh. Ryvkin, Thermodynamics. Statistical Physics and Physical
Kinetics (Mir Publisher, Moscow (1981)).
3). L.D. Landau and E.M. Lifshitz, Statistical Physics. Course of Theoretical Physics.
Volume 5, 3rd edition, (Butterworth-Heinemann, Oxford, UK (1980)).
4). R.P. Feynman, Statistical Mechanics. A set of Lectures (W.A. Benjamin, Inc., Boston,
MA (1972)).
5). H. Eyring, D. Henderson, B.J. Stover and E.M. Eyring, Statistical Mechanics and
Dynamics (J. Wiley and Sons Inc., New York (1964)).

Suggested additional reading on Statistical Physics, Thermodynamics and Physical

Kinetics. Recommended books:
1). M. Planck, Theory of Heat Radiation (Dover, New York (1959)).
2). E.M. Lifshitz and L.P. Pitaevskii, Physical Kinetics. Course of Theoretical Physics.
Volume 8, 3rd ed., Butterworth-Heinemann, Oxford, UK (1981)).
3). D. Ter Haar and H. Wergeland, Elements of Thermodynamics (Addison-Wesley Publ.
Comp., Reading, MA (1966)).

Hydrodynamics and Theory of Elasticity. Recommended books:

1). L.D. Landau and E.M. Lifshitz, Hydrodynamics. Course of Theoretical Physics. Volume
6, 2nd ed., Butterworth-Heinemann, Oxford, UK (1987)).
2). C. Pozrikidis, Introduction to Theoretical and Computational Fluid Dynamics (Oxford
University Press, Oxford, UK (1997)).
3). J.D. Anderson, Fundamental of Aerodynamics, 6th ed., (McGraw-Hill, New York
(2017)).
4). V.P. Korobeinikov, Problems of Point Blast Theory (American Institute of Physics,
New York (1991)).
5). L.D. Landau and E.M. Lifshitz, Theory of Elasticity. Course of Theoretical Physics.
Volume 7, 3rd ed., Butterworth-Heinemann, Oxford, UK (1987)).

Theory of Group Representations and its Applications in Physics. Recommended

books:
1). V.H. Heine, Group Theory in Quantum Mechanics, (Dover Publ. Inc., Mineola, New

6
York (1990)).
2). E. Wigner, Group Theory: And its Application to the Quantum Mechanics of Atomic
Spectra, (Academic Press, New York (1959)).
3). I.M. Gelfand, Minlos and Z.Ya. Shapiro, Representations of the Rotation and Lorentz
Groups and Their Applications (Dover Publishing Inc., Mineola, New York (2018)).
4). N.Ya. Vilenkin, Special Functions and the Theory of Group Representations, 2nd
revised ed., (Amer. Math. Soc., (1983)).
5). A.O. Barut and R. Raczka, Theory of Group Representations and Applications, 2nd ed.,
(World Scientific Publishing, Singapore (1986)).

Suggested additional reading on Theory of Group Representations and its Applica-

tions in Physics. Recommended books:
1). M.A. Naimark and A.I. Stern, Theory of Group Representations (Springer-Verlag, New
York (2011)).
2). M.I. Petrashen and E.D. Trifonov, Applications of Group Theory in Quantum Mechan-
ics, (Dover Publ., Inc., Mineola, New York (2009)). This short, simple and beautiful book
that I used for my special course on Group Representation Theory.

This is a set of seven chapters in Theoretical Physics which I recommend you to know very
well. In particular, it covers the first eight volumes of Landau and Lifshitz. All selected books
contain minimal number of misprints, mistakes and delusions. Therefore, I can recommend
these books for your intense study of theoretical physics. In general, it is better not to
replace these books by others. For instance, the 4th edition of Quantum Electrodynamics
by A. Akhiezer and V.B. Berestetskii, published in 1981 (in Russian) is a great and very
useful book, but it is overloaded with mistakes in the text, equations and references. So, it
better not to choose this book as the first course in Quantum Electrodynamics.
Note also that a number of other important directions, including Nuclear Physics and
Solid State Physics, are missing from our Theorminima. The last two directions cover
more than 80% of all vacancies in modern physics related to the industry. Therefore, it
is important to quickly achieve the required level of competence in these areas. Some
aspects of nuclear physics and theory of solid state are discussed (in fact, at a very good
level) in the books recommended above. But this is clearly not enough, even for everyday

7
communication with specialists actively working in these areas of physics. For instance, I
started to work in the Kurchatov Institute of Atomic Energy, where at that time different
areas of nuclear physics were ‘just a part of life and everyday language’. To cover some
obvious gaps in my education in nuclear physics I have used three following books:
1). J.M. Blatt and W.F. Weiskopff, Theoretical Nuclear Physics, (Dover Publ. Inc., New
York (1999)).
2). A. Bohr and B.R. Mottelson, Nuclear Structure. Single-Particle Motion and Nuclear
Deformations, in two volumes (World Scientific, Singapore (1998)).
3). A. Weinberg and E. Wigner, The Physical Theory of Neutron Chain Reactors, (Univer-
sity of Chicago Press, Chicago, IL (1958)). At the beginning I only read the first part of
this book (‘Fundamental Nuclear Processes in Reactors’). Three years later I studied the
part two (‘Diffusion of Neutrons’), and then (three more years later) my reading of this
wonderful book was over, since I had finished the remaining parts III and IV.

For solid state physics I have used the two following books:
1). A.S. Davydov, Theory of Solid State, (Nauka, Moscow (1976)) [in Russian].
2). J.M. Ziman, Group The Principles of the Theory of Solids, 2nd ed., (Cambridge Univ.
Press, Cambridge, UK (1972)).
In my case these two books were sufficient for a relatively long time. However, I have
to emphasize that the books mentioned above should not be considered as a theoretical
minimum (maybe, only as a part of it) neither for nuclear physics, nor for the theory of solid
state. I am not sure that reading only these books will allow you to conduct independent
research in these areas of physics. These books are only recommended to understand your
colleagues at work, their articles and enter into productive discussions with them at various
seminars, meetings and lectures.

Finally, I want to answer the following question which newcomers always ask me about the
Theorminima. This question is simple: why are you recommending books written only by the
‘old-fashion’ authors? My answer follows from the fundamental difference between the ‘old-
fashion’ (or traditional) authors and authors which represent the ‘new’ (or ‘revolutionary’)
physics. Traditional authors which represent the ‘old-fashion’ physics always consider and
discuss only problems which are absolutely clear for them. In their books they try to make

8
 these problems clear for the rest of us, i.e., for their readers. In contrast with this, the
authors from the new generation discuss problems which are absolutely unclear for them
and in their books they also make these problems completely unclear and very difficult for
their readers.

View publication stats