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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.


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.


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marked as duplicate by CuriousOne, David Z Jul 3 '15 at 9:05

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    $\begingroup$ 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... $\endgroup$ – yuggib Jul 3 '15 at 9:11
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    $\begingroup$ of quantum mechanics in the (very mathematically oriented) Bratteli and Robinson two books. For the more advanced topics, there is time after that ;-) $\endgroup$ – yuggib Jul 3 '15 at 9:13
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    $\begingroup$ 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... $\endgroup$ – childofsaturn Jul 3 '15 at 9:15
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    $\begingroup$ ...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... $\endgroup$ – childofsaturn Jul 3 '15 at 9:19
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    $\begingroup$ ...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... $\endgroup$ – childofsaturn Jul 3 '15 at 9:23