Math QFT Books: Arnold, Takhtajan & Beyond

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SUMMARY

Several key texts provide a mathematical perspective on Quantum Field Theory (QFT), including Dimock's "Algebraic Quantum Field Theory," Rivasseau's works, and Haag's "Local Quantum Physics." Gerald Folland's "Quantum Field Theory: A Tourist Guide for Mathematicians" is highlighted for its rigorous approach, although it does not cover as extensively as traditional physics texts like Schwartz or Peskin and Schroeder. These resources cater to those seeking a deeper mathematical understanding of QFT beyond standard physics curricula.

PREREQUISITES
  • Familiarity with Quantum Mechanics concepts
  • Understanding of Algebraic Quantum Field Theory (AQFT)
  • Knowledge of mathematical rigor in physics
  • Basic principles of Quantum Field Theory (QFT)
NEXT STEPS
  • Explore Dimock's "Algebraic Quantum Field Theory" for foundational concepts
  • Read Rivasseau's texts for insights into constructive QFT
  • Study Haag's "Local Quantum Physics" for advanced AQFT topics
  • Investigate Gerald Folland's "Quantum Field Theory: A Tourist Guide for Mathematicians" for a mathematically rigorous approach
USEFUL FOR

Mathematicians, theoretical physicists, and graduate students interested in the mathematical foundations of Quantum Field Theory and those seeking rigorous texts that bridge physics and mathematics.

Maybe_Memorie
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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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