The Generating Functional of Green Function in Phase Space and Feynman's Rule

On Starting from the generating functional of Green function in phase space and introducing exterior sources for canonical momenta, it turns out that the generating functional of proper vertices is equal to canonical action in tree approximation. The Feyman's rule for the theory in this approximation can be deduced without carrying out explicit functional integration over canonical momenta.A preliminary application for φ⁴-field theory is introduced.