Hi. Can anyone tell me how to solve the path integral(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int D F \exp \left\{ - \frac{1}{2} \int_{t'}^{t} d \tau \int_{t'}^{\tau} ds F(\tau) A^{-1}(\tau - s) F(s) + i \int_{t'}^{t} d\tau F(\tau) \xi(\tau) \right\} [/tex]

In case my Latex doesn't work the integral is over all possible forces F over the functional

\exp \left\{ - \frac{1}{2} \int_{ t' } ^{ t } d \tau \int_{ t' } ^{ \tau } ds F( \tau ) A^{-1} ( \tau - s ) F( \tau) + i \int_{ t' } ^{t} d \tau F( \tau ) \xi ( \tau ) \right\}

I have tried to solve it by making the discrete Fourier transform of the functions F, A^{-1} and \xi but I run into some trouble when doing that.

/Jezuz

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Path integral over probability functional

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**