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Gaussian functional integral with constant operator

  1. Feb 13, 2015 #1
    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. jcsd
  3. Feb 19, 2015 #2
    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?
     
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