# Gaussian Functional Integral

1. Nov 26, 2014

### psi*psi

I am new to path integral and struggling with the computation involving Gaussian functional integrals. Could anyone show me the steps of computing the following integral?
$$\int D \phi e^{-S},$$
where
$$S = \int dx~d \tau [(\frac{\partial \phi}{\partial x})^2+2 i \frac{\partial \theta}{\partial \tau} \frac{\partial \phi}{\partial x} ]$$.
$\theta$ is a function that is not being integrated over.
I know I am supposed to use the formula
$$\int D v(x) \mathrm{exp}[-\frac{1}{2} \int d x d x'~v(x) A(x,x') v(x') + \int d x~j(x) v(x)] \propto \mathrm{exp} [\frac{1}{2} \int d x d x'~j(x) A^{-1}(x,x') j(x')],$$
where $A(x,x')$ is an operator. But I am having trouble in applying this result.

2. Dec 2, 2014

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?