# Gaussian functional integral with constant operator

1. Feb 13, 2015

### Einj

Hello everyone. What it the result for a Gaussian functional integral when the "matrix" is nothing but a number? Mathematically speaking is the following true?

$$\int \mathcal{D}\phi e^{-\int d^3k f(k) |\phi(k)|^2}\propto \left(f(k)\right)^{-1/2}$$

Here $f(k)$ is just a function of k, not derivatives or operators etc... I'm asking this because in principle we should have a determinant of the "matrix" and I don't know if what I wrote is correct.
Thanks!

2. Feb 19, 2015