In this paper, the interaction of electron and phonon in metals is expressed using Hamiltonian operator as follows. By excahnging phonon energy with in the vicinity of isotropical Fermi surface and using following electron and hole operators. We obtain the interaction of electron and phonon. And new Feynman Graphs are tried with the following conditions on. First, when state transfer state, phonon cannot be created. Second, when state transfer state, phonon cannot be destroyed. Third, when state transfer state, phonon can be created or destroyed. Fourth, when state transfer state, phonon can be created or destroyed.