Timeline for Feynman Kac Formula as appears in Krzysztof Gawedzki's Lectures on conformal field theory
Current License: CC BY-SA 2.5
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| Jun 8, 2010 at 11:00 | comment | added | David Bar Moshe | In the following lecture notes in math. by Albeverio, Høegh-Krohn, Mazzucchi, chapter 10.4.2 treats the path integrls within (Gaussian) white noise analysis. In addition in section 10.4.4 there is an approach based on Poisson processes. books.google.com/… | |
| Jun 8, 2010 at 10:59 | comment | added | David Bar Moshe | The answer is given in two comments: The following two lecture notes by Mikko Lane contain a heuristic description the use of Fourier analysis to evaluate the Harmonic oscillator path integral. The required two point function is given only as an exercise, but I think that it is clear how to apply the same method for its evaluation. physik.uni-bielefeld.de/~laine/thermal/lec01.pdf physik.uni-bielefeld.de/~laine/thermal/lec02.pdf | |
| Jun 7, 2010 at 16:30 | comment | added | John Jiang | Thanks for the great reference. I guess what I really would like to understand is how to use fourier transform to rewrite the left hand side: $$\int_{C_{\rm{per}[0,L]}} \phi(x_1) \phi(x_2) d\mu_(\phi)$$ Also are there good references that systematically explore the connection between Gaussian processes and Feynman path integrals accessible to probabilists? | |
| Jun 7, 2010 at 14:46 | history | answered | David Bar Moshe | CC BY-SA 2.5 |