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Feynmann path integral

  1. Nov 17, 2006 #1
    Is there any Functional equation In functional derivatives so the Feynmann Path integral is its solution?.. i mean given:

    [tex] A[\Phi]=\int \bold D[\Phi]e^{iS/\hbar} [/tex]

    Then A (functional) satisfies:

    [tex] G( \delta , \delta ^{2} , B[\phi] )A[\Phi]=0 [/tex]

    where B is a known functional and "delta" here is the functional derivative.
  2. jcsd
  3. Nov 17, 2006 #2
    I think there would be some difficulty in defining such a thing since the path integral isn't technically an integral at all, since it's defined over a space with no clearly defineable measure.
  4. Nov 18, 2006 #3


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    If you take this A to be the vacuum to vacuum transition amplitude then this equation exists and as far as I know it is known as Dyson-Schwinger equation. You can find the derivation in section 6.4 of Ryder's "Quantum Field Theory".
    Last edited: Nov 18, 2006
  5. Nov 19, 2006 #4
    "Hellfire" is the Dyson-Schwinger equation a method to evaluate propagators (Non-perturbative) without recalling to Path Integrals?? :confused:
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