Quantum Field Theory Description of the Interaction System of Electrons-Photon-Phonon

A Lagrangian in relativestic covariant formalism which desctibes the interaction system of electrons-photon-phonon is proposed. The expressions are obtained for energy, momentum and angular momentum of the system. This Lagrangian is singular in sense of Dirac. The Faddeev-Senjanovic path-integral quanhzation of this system is performed. The generator for gauge transformation of this system is derived. The phase-space generating functional of the Green function of this system is deduced. Applying the Green function approach in field theory, we get energy spectrum and particle distribution function.