Quantum Field Theory for Mathematicians

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About Robin Ticciati. Robin Ticciati. Books by Robin Ticciati. Trivia About Quantum Field The This is a great place to start if you want to study the recent work of Jacob Lurie on the classification of topological quantum field theories. The only problem with this book is that it doesn't say much about how quantum field theories are used to compute invariants of topological spaces. I therefore think it's best to supplement this book with something else -- perhaps the classic paper of Atiyah.

This was meant to be a comment, not an answer, but I don't have enough reputation.

Basically, I did a masters in maths pure maths , then a masters is physics QFT , then a PhD in maths pure, algebraic geometry stuff. So, I had to grapple with the issue you are trying to solve.

A Bridge between Mathematicians and Physicists

I think it will be hard to get a good answer since you don't specify for what reason you want to learn QFT. Some comments then:. If you are going to work on things like Seiberg-Witten equations from a math perspective, then I suppose the book of Baez and Muniain called Gauge Fields, Knots and Gravity mentioned by Bob Jones above is great since you will not need to quantize things anyways. If you actually want to get an understanding of the subject that includes the physics perspective which is what I tried to do , then I suggest developing some physics background.


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Actually, I tried to follow at the same time a more "mathematically precise" approach to QFT - but in the end I thought this was harder than the physics approach - because, I think, you end up spending an enormous amount of time to get anywhere, and risk the change of being buried in a pile of math formalism before being able to do simple computations.

A last comment. In my experience, it was great to talk to physicists they tend to be more chatty and tell more stories about their subject than mathematicians. However, one will need to have covered some Quantum Mechanics previously. The book was originally recommended to me. It's great in the sense that it is quite rigorous and self-contained, and yet quite broad in its presentation. A bit more engaged and lengthy presentation with specific topics is "Quantum Fields and Strings: A Course for Mathematicians".

This is a 2-volume set filled with lectures by people in the field. Quite technical though. This answer contains some additional resources that may be useful.

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Please note that answers which simply list resources but provide no details are strongly discouraged by the site's policy on resource recommendation questions. This answer is left here to contain additional links that do not yet have commentary. For Supersymmetry which, as Alexander Braverman rightly said, is most important for mathematical applications , the book by Dan Freed ["Five Lectures on Supersymmetry".

Formalizing Quantum Field Theory ;. Rigor in quantum field theory ;. CFTs and formalizing quantum field theory. Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site the association bonus does not count.

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Would you like to answer one of these unanswered questions instead? Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Quantum Field Theory from a mathematical point of view Ask Question. Asked 7 years, 11 months ago. Active 1 year, 4 months ago. Viewed 24k times. Being a student of mathematics myself, I understand how frustrating it can be to learn physics from a physicist, but at the end of the day, it will make learning QFT or any subject of physics for that matter much easier if you understand the physical meaning of the subject and why you are doing what you are doing.

In any case, it will certainly improve your appreciation of the subject. Maybe I can provide a little motivation, before adding to the list of recommended reading. The others are all published books.

As for books, I've seen both Amazon and Google books links on other stackexchange sites In fact, stackexchange automatically converts Amazon links to affiliate links and gets money from any purchases. This December an AMS volume appears that collects surveys and original articles on this topic: Sati, Schreiber eds.

Quantum Field Theory I: Basics in Mathematics and Physics

Urs Schreiber. There's certainly few independent things the question may refer to, perhaps the dychotomy is between foundations and applications of QFT. Both subjects can but don't have to be useful and interesting. Where do you sense polemics? I remember writing something along these lines two years ago at the nCafe :- golem.

I have added a comment to the bottom of my answer above in an attempt to clarify this. I think it is important to realize that much of physics, even the most established theories, is "vague and speculative" from the point of view of actual mathematics, of actual precision of argument and certainty of truth. This is not at all to say that this physics is bad. But realizing this gap to the non-vagueness and non-speculation of maths is the necessary first step for appreciating what it means -- or would mean -- to genuinely have "QFT from a mathematical point of view".

I'd probably prefer heuristic to vague and speculative, which implies degree of uncertainty that is not appropriate. I also think the two efforts are not distinct - if you want to make the heuristic structure of QFT which nonetheless is efficient in producing true mathematical statements more precise, perhaps the first logical step is learning what it is.

Pieter Naaijkens. Varadarajan Mirror Symmetry by C. Vafa, E. Zaslow, et. Gross The first book develops some of the analysis necessary for CFTs Chapter 8 as well as the theory of conformal compactifications Chapters 1, 2 and the theory of the Witt and Virosoro Algebras Chapters Tarun Chitra. Bob Jones. Some comments then: If you are going to work on things like Seiberg-Witten equations from a math perspective, then I suppose the book of Baez and Muniain called Gauge Fields, Knots and Gravity mentioned by Bob Jones above is great since you will not need to quantize things anyways.

Kevin Costello , a mathematician, has written a book on quantum field theory, particularly the perturbative aspects. The book used to be available from his web page, but it has now been published by the AMS. You can find the links in his webpage to which I linked above.

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So far 3 volume appeared and are available also via springerlink. This work is quite accessible for a mathematician. An excellent introduction to the mathematics of QFT which is truly a textbook which can for instance serve as support material in a 1st or 2nd year graduate course in mathematics is "Quantum Mechanics and Quantum Field Theory, A Mathematical Primer" by Jonathan Dimock , Cambridge University Press, Featured on Meta. Unicorn Meta Zoo 8: What does leadership look like in our communities?


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