# Feynmann path integral

1. Nov 17, 2006

Is there any Functional equation In functional derivatives so the Feynmann 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.

2. Nov 17, 2006

### StatMechGuy

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.

3. Nov 18, 2006

### hellfire

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
4. Nov 19, 2006