1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Evaluating Functional integrals

  1. Aug 11, 2007 #1
    HOw can you compute a Gaussian functional integral?

    i mean integral of the type [tex] e^{-iS_{0}[\phi]+i(J,\phi)} [/tex]

    if J=0 then i believe that we can describe the Functional integral as

    [tex] \frac{c}{(Det(a\partial +b)} [/tex] a,b,c constant

    so [tex] Det(a\partial +b)}= exp^{-\zeta '(0)} [/tex]

    [tex] \zeta (s) = \sum_{1 \le n}\lambda_{n} ^{-s} [/tex]

    my problem comes when J(x) is different from 0 so we have a functional determinant which is also a function (functional ?? ) of J(x) , then how could yo evaluate it?, also a Fourier transform of a gaussian is again another Gaussian.

    Another question..how can you once you have obtained the functional integral Z[J] expressions of the form

    [tex] \frac{ \delta ^{n}Z[J]}{ \delta J(x1) \delta J(x2)........} [/tex]

    so you get finite results ??
     
    Last edited: Aug 11, 2007
  2. jcsd
  3. Aug 11, 2007 #2

    f-h

    User Avatar

    You can't except perturbatively. The perturbation expansion is explained in any good book on QFT, try Zee's QFT in a Nutshell for example.
     
  4. Aug 11, 2007 #3

    f-h

    User Avatar

    Sorry I see I misread, the trick is to complete the square. You add J^2 - J^2 write the whole thing as (phi + J)^2 and pull the J^2 term out of the integral.
     
  5. Aug 11, 2007 #4
    thank you everybody.. f-h hit the correct answer (thankx) however still we have the problem that how could you evaluate the functional Determinant.

    [tex] Det( a\partial ^{2} +b) [/tex] of the operator:

    [tex] ( a\partial ^{2} +b)(\phi +J(x))[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Evaluating Functional integrals
  1. Evolution function (Replies: 2)

  2. Grassmann integration (Replies: 5)

Loading...