Physics textbooks for self-study

Here are some physics textbooks that I’ve read over the years. Each textbook is rated from 1-5 Diracs (Paul_Dirac,_1933.jpg) on quality for self-study. Most topics are divided into (basic) and (advanced).

Screen Shot 2020-01-04 at 11.43.27 AM
Figure 1. Areas of physics (biased toward high-energy theory). Special relativity and electromagnetism can be learned separately but complement each other. “Weak prerequisites” are math subjects that can usually be learned as you go along.

Tips for self-study:

  • Shorter is better when it comes to textbooks. The problem with self-study is missing the forest for the trees. Most textbooks can give you the details, but there is no one to explain how to fit the information in your head in a compact and memorable way. Shorter books are usually better for this. The flip side is that shorter books are harder to understand if you have no past exposure. Start by reading parts of a standard textbook to get the basics, then go back.
  • Do enough exercises. But don’t feel the need to do every single one before moving on, even if you are a little confused. It can be more efficient to just keep going, since physics is interconnected and the new material often clarifies the old.
  • Write notes in the margins of any confusing aspects of derivations or errata you discover. These will undoubtedly help you when you revisit them years later.

Personal (controversial) opinions:

  • Avoid mathematical physics-oriented books. When I started out, I thought more rigor can never hurt. But if you are interested in physics, learn physics. Math books often dwell on excessive formalism that is irrelevant for physics at the end of the day.
  • Amazon ratings are useless. Unless they’re really terrible, most books will have very good ratings. I suspect most reviewers used the book for a class, are already experts on the subject, or simply want to look smart. 🙃

Quantum mechanics (basic)

Griffiths, Introduction to Quantum Mechanics (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

I start by contradicting my own advice about shorter books. 😀  This is a long but very readable book that is even worth reading from cover to cover. There is a reason this is the standard textbook in many places. One tends to forget how much it covers: statistical mechanics, spontaneous and stimulated emission, band structure, WKB approximation… Not in great detail, but often enough.

Quantum mechanics (advanced)

Weinberg, Lectures on Quantum Mechanics (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

Weinberg’s books are known for their slow and systematic presentation. If you’re in a rush, my recommendation is to just read chapters 3 and 4, which contain the essentials of quantum mechanics and spin and are relatively self-contained.

Linear algebra (basic)

Strang, Introduction to Linear Algebra (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

Actually, I suggest the lectures instead of the book. One relaxing 45-minute lecture a day and you’ll know linear algebra in a month.

Classical mechanics (advanced)

Landau and Lifshitz, Mechanics (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

The Russian school excels at explaining things deeply and simply. The first two chapters contain the best exposition of classical mechanics there is. In my experience, even professional physicists are often confused by some foundational topics that are explained here. (For example, where does the Lagrangian \frac{1}{2}mv^2 come from? Answer: Homogeneity+isotropy of space, and Galilean invariance. Together with the principle of stationary action, this leads to F=ma.) If you’ve never seen a Lagrangian before, start with one of the numerous intros, like this one.

Special relativity (SR)/Electromagnetism (advanced)

Landau and Lifshitz, The Classical Theory of Fields (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

Amusingly, this does not actually cover the simplest classical field theories (scalar fields) since the only relevant classical fields in practice are the electromagnetic and gravitational. Chapters 1-4 are an excellent exposition of SR and how E&M fits into it, while chapters 10-12 are a decent introduction to general relativity that complements other texts.

General relativity (GR)

Dirac, General Theory of Relativity (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

Who said GR is hard to understand? This pamphlet by the big man himself weighs in at only 69 pages. Unlike most books, it explains curved spacetime as a surface embedded in a higher dimensional space with flat metric. In my view, this is the most intuitive way to understand it. Among other things, it leads to the covariant derivative as the projection of the directional derivative onto the tangent space, a very pleasing interpretation of an otherwise confusing concept.

No exercises though. So as an introduction, you will want:

Zee, Einstein Gravity in a Nutshell (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

This is the book I wish I had when starting GR. Zee is one of the most gifted physics expositors of our time. Unfortunately, it is rather long, so I would recommend first reading enough of this one to understand Dirac, then going back to this one for special topics.

Carroll, Spacetime and Geometry: An Introduction to General Relativity (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

This was my first exposure to GR. I got through about chapter 3 before getting confused and stopping. This is one of those mathematical physics books I mentioned above, with a lot of formalism surrounding manifolds, tensors, and differential forms at the outset. It is good to know eventually, but not what you need as an introduction. I suppose it would make a good reference, but Zee’s book also serves well in this regard.

Quantum field theory

The subjects above are all well-established and have a fairly defined “core”. On the other hand, QFT is an evolving field with a sprawling mess of important results. Each textbook emphasizes different aspects, so you will need multiple books.

Zee, Quantum Field Theory in a Nutshell (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

This was my first and favorite QFT book. Other textbooks have more detail, but none will make you fall in love with the subject like this one. Just get it and enjoy the magic of the path integral.

Schwartz, Quantum Field Theory and the Standard Model (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

This is a very thorough textbook, perhaps the modern successor to the classic Peskin and Schroeder. I particularly enjoyed the bottom-up construction of spin 1 and 2 Lagrangians in chapter 8. One criticism is that many calculations are rather clunky and involved. For example, scalar QED is heavily used, which is conceptually simpler but involves more diagrams than spinor QED. I prefer Zee’s approach of just starting with spinor QED.

(Also, his notation with all indices on the same level bugs me…)

Srednicki, Quantum Field Theory

No rating for this one since I haven’t read it in much detail. The first chapter (“Attempts at relativistic quantum mechanics”) is an excellent motivation for QFT. The chapters are short and to the point. If I could start over, I would probably read this one concurrently with Zee.

Group theory

Zee, Group Theory in a Nutshell for Physicists (Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg Paul_Dirac,_1933.jpg)

For those like me that get bored to death reading pure math textbooks, Zee’s usual colloquial style makes even classifying representations of finite groups exciting. Not absolutely necessary to read if you’re in a hurry to learn more physics, but still a joy.


Advanced resources

Once you have a grasp of the areas above, additional topics can be learned without having to rearrange your entire worldview (with the possible exception of string theory). Here are some of my favorite advanced resources.

Shifman, Advanced Topics in Quantum Field Theory

Despite the title, this book focuses on simple explanations of modern topics without arduous derivations. Some interesting results cannot be found elsewhere, e.g. that domain walls antigravitate!

Terning, Modern Supersymmetry: Dynamics and Duality

This is a compact volume on supersymmetric field theory. The first three chapters are quite good, but I found some explanations in later chapters hard to understand. A better intro to Young tableaux is found here.

Polchinski, String Theory Vols. 1 and 2

This labor of love by the father of D-branes himself covers pre-AdS/CFT string theory. It seems to be the standard textbook on the subject, for good reason. The explanations are clear and the text contains many invaluable exercises. His passion for the topic is evident throughout.

Hartman, Lecture notes on quantum gravity and black holes

Not a textbook, but a good set of lecture notes by Tom Hartman. Explores many contemporary topics that have yet to make it into any textbooks I know of. Many useful exercises are included.

2 thoughts on “Physics textbooks for self-study

  1. As a fellow self studier I fully agree with all the tips you posted except the one about mathematical physics. I contrast myself to you with that I am interested in mathematics and use physics for applications (very useful in geometry and topology) and hence come from a different viewpoint. However I believe that mathematics is important as it provides justification for steps in logic when you do proofs or solve problems and in general is good for teaching logical thinking. You state that these books `dwell on excessive formalism that is irrelevant`, could you give any examples?

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    1. Yes, I gave Carroll’s GR book as an example in the post.

      I am certainly not against rigorous thinking. But I find that physicists are generally better than mathematicians at explaining the “meat” of an idea, rather than listing definitions/theorems and playing around with notation.

      For example, I once laboriously worked through this differential geometry text [1]. The sections on differential forms were long and boring. In contrast, Zee’s QFT book (p.246) gives a better explanation in just 2 pages(!), which actually shows why we define them with their properties.

      [1] http://pi.math.cornell.edu/~sjamaar/manifolds/manifold.pdf

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