# Evaluating a infinite-dimensional Gaussian integral

1. Nov 7, 2006

Hello,.. that's part of a problem i find in QFT (i won't explain it since it can be very tedious), the question is that i must evaluate the Multi-dimensional Gaussian Integral.

$$\int_{-\infty}^{\infty}d^{n}V exp(x^{T}Ax)exp(ag(x))$$

for $$n\rightarrow \infty$$ of course if the integral is "purely" a Gaussian then you can do it.. however you have the problem of g(x), if you think you're integrating about 2paths" (trajectories), then my idea is that perhaps you could consider "functional integration" under a infinite dimensional Gaussian Borel Meassure, however i don't know more, i have the "(approximate) meassure but don't know any Numerical method valid for infinite dimensional spaces if a is small a Gaussian meassure could work but how do i perform the integral?.. thankx

2. Nov 5, 2010

### babamarysol

$$\int dq_{1} dq_{2} (q_{1}^{2} + q_{1}q_{2}) exp[\mathbf{q}^{T}\mathbf{A}\mathbf{q}]$$