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EDIT: I was aware of the supposed duplicate. But I'm interested in a clear and focused path through the basics to advanced theoretical physics such as string theory - a path that avoids studying engineering physics - for a pure mathematician with no physics background. I can't see in the supposed duplicate where this path is outlined.

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I'm a pure mathematics PhD student in Riemannian geometry / geometric analysis. My main interests are in Einstein manifolds, Ricci flow, harmonic maps, and Yang-Mills theory.

I have no training whatsoever in physics: I've never even picked up the typical 1,500 page textbook titled Physics for Scientists and Engineers etc. I've only ever read pure mathematics and can handle any level of pure mathematics to any level of abstraction.

I'd like to learn the background and basics in theoretical physics motivating the above areas of geometric analysis to develop physical intuition: general relativity, gauge field theories, and the standard model of particle physics, etc. Ideally I also want to learn advanced theoretical physics such as quantum field theory, string theory, and sypersymmetry. I'd like a structured path through basic to advanced theoretical physics for a mathematician with no physics training.

I have looked at many standard references in these areas but their assumptions on the physics background of the reader does not align with my background. These standard references all start talking and explaining things in physics notation, terminology, concepts, and intuition that is assumed on the reader.

Question: As a pure mathematician, how do I learn basic through to advanced theoretical physics in an clear, focused and structured way? What books should I read? Are there books tailored to a target audience like myself: a pure mathematician with no physics background?

If required, I'm happy to start from scratch by working through a 1,500 page physics textbooks. However, after progressing through mathematics one realises that starting with working through the typical 1,500 page calculus textbook, such as Stewart Calculus, is unnecessary because those books are tailored to engineers. Instead, one can start with a book on set theory, proof, and logic, and then go straight into standard undergraduate books like Rudin Principals of Mathematical Analysis and Herstein Topics in Algebra, etc. Indeed, many universities offer a streamlined program of study for pure mathematics majors that avoids wasting time on engineering calculus.

Question: Is it the same situation in physics? Are those 1,500 page physics textbooks targeted mostly at engineers and is there a focused and streamlined path through theoretical physics that starts at the start of theoretical physics and gets to advanced theoretical physics such as quantum field theory and string theory without having to learn engineering physics?

I would be VERY grateful for someone to provide some book recommendations and possibly a structured path for achieving the above.

Qmechanic
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mdg
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  • Since you want my opinion: physics books aimed at "scientists and engineers" are a waste of time and so is trying to learn physics out of books alone. You may be able to learn some mathematical physics out of books, but physics is an interactive scientific exercise that requires you to play with others, so you might as well learn from them right away. Math, I was told, at its best is very much the same... – CuriousOne Jul 03 '15 at 09:05
  • Physics doesn't depend on your background. It only depends on nature. – CuriousOne Jul 03 '15 at 09:10
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    I would use the theoretical physics course of L.Landau as a first approach to the topics of theoretical physics (for your purposes the first four books-classical mechanics, relativity/classical field theory, quantum mechanics, relativistic quantum mechanics-should suffice, probably just the first three). For classical mechanics with a more geometrical flavor you should look the V. Arnold book "mathematical methods of classical mechanics" (or a similar title). After knowing basics of QM (as in Landau), you may look for the algebraic approach... – yuggib Jul 03 '15 at 09:11
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    of quantum mechanics in the (very mathematically oriented) Bratteli and Robinson two books. For the more advanced topics, there is time after that ;-) – yuggib Jul 03 '15 at 09:13
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    Indeed working through a typical freshman/sophomore level physics book would be a waste of time: No one who works on abstract theoretical physics topics such as supersymmetry and string theory ever uses the "Lensmaker equation" or stuff about heat engines in their research (however topics like classical mechanics and electromagnetism do help in developing physical intuition to an extent, so study those if you can) So indeed your guess is correct in that you can jump straight into the more abstract treatments. Now let me make some recommendations. For classical mechanics, the basic thing you... – childofsaturn Jul 03 '15 at 09:15
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    ...need to internalize is symmetry and variational principles, as they are at the heart of physics. Landau/Lifschitz (not all the chapters are necessary though) is a good start followed by a more geometric treatment (like Arnold's). You can continue your study of mechanics with other "classical" topics such as electromagnetism, gauge theory and general relativity. I found "Gauge Fields, Gravity and Knots" by Baez to take a good middle ground between math and physics (it also provides good references). For a more thorough treatment of General Relativity, Wald's book is as good as it gets for... – childofsaturn Jul 03 '15 at 09:19
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    ...a book written by a physicist when it comes to rigor. For the more quantum topics, chapters 8-10 of "Mirrror Symmetry" by Vafa, Hori, Zaslow et al (a book aimed at both mathematicians and physicists) should provide a very quick introduction to quantum mechanics, supersymmetry and path integrals, though it would probably need to be supplemented. For more detailed treatment of QM I recommend Shankar. QFT is always a tricky subject and no one book is good enough. I like Tom Banks' book and also Pierre Ramond's book, and Mirror Symmetry also provides a good picture. Finally a very advanced... – childofsaturn Jul 03 '15 at 09:23
  • @mdg: You wanted to know how people learn physics. They learn physics by working on physics problems with others, first on test problems, then on real ones. A typical physics problem these days is attacked by multiple, sometimes tens of thousands of physicists. You can count the number of authors' names on key papers, that's a pretty good indicator. – CuriousOne Jul 03 '15 at 09:25
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    ... for all these topics is "Quantum Fields and Strings: A course for mathematicians" which was aimed at exactly what you mention: Training mathematicians to develop physical intuition and familiarizing them with modern methods (Volume 2 is more "physicsy"). It's extremely dense and quite advanced, so I would probably look at more elementary texts first. – childofsaturn Jul 03 '15 at 09:25
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    See: http://physics.stackexchange.com/q/6047/, http://math.stackexchange.com/q/15890/, http://math.stackexchange.com/q/89694/. – mdg Jul 03 '15 at 10:00
  • There is no such thing. Science is a creative mess and I can guarantee that you will end up highly educated on structural issues but without the ability to tell me what the second law of thermodynamics means in six words or less. :-) – CuriousOne Jul 03 '15 at 20:08
  • You don't agree but you can't tell me in six words or less what the second law of thermodynamics is? OK. I think we should stop on that high note and good luck with your studies of "physics". :-) – CuriousOne Jul 03 '15 at 20:34
  • I answered this at http://www.physicsoverflow.org/32400 – Arnold Neumaier Jul 11 '15 at 13:44

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