The J. Schwinger’s formalism of the Green function in the quantum electrodynamics is applied to the transition problem of the state. It is shown that the many body kernel in the Heisenberg representation involves the information about the transition of the state and this is directly represented by the repeated use of the one body kernel G, G and the vertex operator Γµ defined by J. Schwinger. Further, the renormalization is discussed without use of the usual perturbation theory, although there remains the difficulty associated with the b-divergence.