What Are the Best Books for Learning Path and Functional Integration?

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SUMMARY

This discussion focuses on the best resources for learning about path and functional integration, particularly in the context of quantum field theory (QFT). While QFT books provide a foundational understanding, they often lack rigorous mathematical treatment, particularly regarding infinities in integration measures. For a more mathematically sound approach, users are directed to explore articles on ArXiv, specifically searching for "path integral" under the Mathematics category. Notable references include math-ph/0012017, which discusses advancements in making the Feynman path integral mathematically rigorous.

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT)
  • Familiarity with mathematical concepts related to integration
  • Knowledge of Feynman path integrals
  • Basic proficiency in searching academic databases like ArXiv
NEXT STEPS
  • Research articles on ArXiv related to "path integral" in the Mathematics category
  • Study the mathematical rigor of Feynman path integrals through referenced papers
  • Explore advanced QFT textbooks that address integration measures
  • Investigate the implications of infinities in quantum integration techniques
USEFUL FOR

Students and researchers in theoretical physics, mathematicians interested in integration techniques, and anyone seeking a deeper understanding of path and functional integration in quantum mechanics.

Dahaka14
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Can anyone suggest any good books on learning path integration? Maybe even just functional integration? I understand that there may be good introductions in QFT books, but are there any good mathematical approaches to these concepts contained in other books? Please tell me if just reading good QFT books will suffice. Thanks.
 
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If you just want to use them, reading some good QFT books will serve you just fine. However, even in the best of QFT books, usually a lot of things are swept under the carpet (most notably: some possible infinities in the integration measure).
If you want a mathematically rigorous treatment, I cannot really help you, except to refer you to the ArXiv (www.arxiv.org[/url]). If you use the search form and search for "path integral" in the title and check only the Mathematics box, you might find some interesting articles. For example, in [url=http://arxiv.org/abs/math-ph/0012017v1]math-ph/0012017[/URL] I find
[quote]
Since Feynman’s invention of the path integral, much research
have been done to make the real time Feynman path integral mathematically rigorous (see [6], [9], [10], [13],[18], [19], and [20]).
[/quote]
So you might check out those references, for starters.
 
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