Functional Equation & Feynman Path Integral Solution

Karlisbad
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Is there any Functional equation In functional derivatives so the Feynman Path integral is its solution?.. i mean given:

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

Then A (functional) satisfies:

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

where B is a known functional and "delta" here is the functional derivative.
 
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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.
 
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".
 
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"Hellfire" is the Dyson-Schwinger equation a method to evaluate propagators (Non-perturbative) without recalling to Path Integrals?? :confused:
 
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