Math QFT Books: Arnold, Takhtajan & Beyond

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The discussion centers on the search for quantum field theory (QFT) books that approach the subject from a mathematical perspective. Recommendations include Dimock's book, which incorporates QFT within the context of constructive quantum field theory (CQFT), and Rivasseau's work, also aligned with CQFT. Haag's book on algebraic quantum field theory (AQFT) is noted as another significant resource. Gerald Folland's "Quantum Field Theory: A Tourist Guide for Mathematicians" is highlighted for its balance of mathematical rigor and practical calculations, although it does not cover as extensively as some physics-focused texts. The conversation reflects a desire for more mathematically rigorous treatments of QFT, emphasizing the challenges in achieving such rigor in the field.
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Are there any QFT books written from a mathematical perspective? Something in the same vain as V. Arnolds Mechanics and Takhtajan's QM.

Thanks.
 
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You might be interested in Quantum Field Theory: A Tourist Guide for Mathematicians by Gerald Folland

https://www.amazon.com/dp/0821847058/?tag=pfamazon01-20

Although Folland doesn't cover as much as physics texts such as Schwartz or Peskin and Schroeder, Folland does cover a lot more than most rigourous math books on quantum field theory. Folland uses mathematical rigour where possible, and where physicists' quantum field theory calculations have yet to be made mathematically rigourous, Folland states the mathematical difficulties, and then pushes through the physicists' calculations.

I've been waiting for many years for someone to write this book, and now I don't have time to read it.
 
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