Path integral over probability functional

by Jezuz
Tags: functional, integral, path, probability
Jezuz is offline
May22-06, 12:18 PM
P: 31
Hi. Can anyone tell me how to solve the path integral

[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.

Phys.Org News Partner Science news on
Lemurs match scent of a friend to sound of her voice
Repeated self-healing now possible in composite materials
'Heartbleed' fix may slow Web performance

Register to reply

Related Discussions
a functional that depends on an integral? Calculus 3
Help with this path integral. Quantum Physics 2
Path integral Quantum Physics 3
Functional integral (semiclassic formula) Quantum Physics 2
Path Integral Development Quantum Physics 3