HOw can you compute a Gaussian functional integral?(adsbygoogle = window.adsbygoogle || []).push({});

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 ??

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# Evaluating Functional integrals

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