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Evaluating a infinite-dimensional Gaussian integral

  1. Nov 7, 2006 #1
    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.

    [tex] \int_{-\infty}^{\infty}d^{n}V exp(x^{T}Ax)exp(ag(x)) [/tex]

    for [tex] n\rightarrow \infty [/tex] of course if the integral is "purely" a Gaussian then you can do it..:redface: :smile: 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 :confused: :confused: if a is small a Gaussian meassure could work but how do i perform the integral?.. thankx
     
  2. jcsd
  3. Nov 5, 2010 #2
    can you tell me something about this

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

    ?
     
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