Path integral methods

Question

Are there detailed expositions of the path integral methods in (mathematical) physics other than Feynman-Hibbs and Glimm-Jaffe?

There are several references contained in answers to relevant questions here on MO, for example http://mathoverflow.net/questions/19495/mathematics-of-path-integral-state-of-the-art or http://mathoverflow.net/questions/24823/the-mathematical-theory-of-feynman-integrals — მამუკა ჯიბლაძე, Dec 19 '15 at 17:33

score 4 · Answer 1 · answered Feb 10 '16 at 21:41

Hagen Kleinert

Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets

http://users.physik.fu-berlin.de/~kleinert/kleinert/?p=loadbook&book=8

http://www.amazon.com/Integrals-Quantum-Mechanics-Statistics-Financial/dp/9814273562/ref=asap_bc?ie=UTF8

that book seems most comprehensive

score 4 · Answer 2 · answered Feb 22 '16 at 15:17

4

Of course the physics literature is full of references on path integrals. One would not know where to start. Kleinert's books suggested by Alexander must be a good choice. On the rigorous side you might want to have a look at:

"Functional Integration and Quantum Physics" by Barry Simon, Academic Press 1979.
"Feynman-Kac-Type Theorems and Gibbs Measures on Path Space" by Lorinczi, Hiroshima and Betz, De Gruyter 2011.

answered Feb 22 '16 at 15:17

Abdelmalek Abdesselam

21,801

1

Just to briefly indicate that there is a second edition of Simon's book (AMS Chelsea, 2004). – Umberto Lupo Feb 22 '16 at 16:26

score 4 · Answer 3 · answered Feb 23 '16 at 18:53

An impressive list of references to complement the answers already given can be found at the bottom of the following Scholarpedia article by Sergio Albeverio and Sonia Mazzucchi. The approach to path integrals based on "cylindrical measures", aka "promeasures", is not discussed in the body of the article but can be read about in the work by DeWitt-Morette and collaborators referenced there.

Path integral methods

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