Based on the phase space generating functional of Green function for a system with regular Lagrangian

using saddle point approximation

we have been shown that the generating functional of proper venices is equal to canonicsl action in tree approximation. The Feynman’s rule for the theory can be deduced in this approximation without carrying out explicitly path integral over canonical momenta. A preliminary application of the theory to the Lagrangian which differs from harmonic oscillator by a total differential term of time was given

the propagator and energy level are different in both case.