Path/Functional Integration

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In summary, the conversation discusses the topic of learning path integration and functional integration in the context of quantum field theory (QFT). The speaker asks for recommendations on books that cover these concepts, particularly ones with a strong mathematical approach. The responder suggests that reading QFT books can suffice for practical use, but for a more rigorous understanding, they recommend checking out articles on the ArXiv website that focus on the path integral and its mathematical rigor. Several references are mentioned for further exploration.
  • #1
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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I am happy to provide some suggestions for books on learning path and functional integration. While QFT books may provide a good introduction to these concepts, there are also other books that offer a more mathematical approach.

One book that I would recommend is "Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets" by Hagen Kleinert. This book offers a comprehensive and rigorous treatment of path integrals, from the basics to advanced topics, and includes applications in various fields.

Another useful text is "Functional Integration and Quantum Physics" by Barry Simon. This book focuses on the mathematical foundations of functional integration and its applications in quantum physics.

For a more general introduction to path and functional integration, "Quantum Field Theory for the Gifted Amateur" by Tom Lancaster and Stephen J. Blundell is a great resource. It provides a clear and accessible explanation of these concepts, as well as their applications in quantum field theory.

In summary, while reading good QFT books may suffice for an introduction to path and functional integration, there are also other books that offer a more focused and rigorous treatment of these concepts. I hope these recommendations are helpful in your learning journey.
 

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