Quantum field theory for a system of interacting photons, electrons, and phonons

Abstract

A Lagrangian in (1 + 3)-dimensional space-time which describes the interaction of photons, electrons, and phonons is proposed. This is a generalization of Rodriguez-Nunez' model. This Lagrangian is also singular in the sense of Dirac. The path-integral quantization of this system is performed with the aid of the Dirac formalism for a singular Lagrangian and the method of functional integration. The phase-space generating functional of the Green function of this system is deduced. The Ward identities in canonical formalism for local symmetries are derived, and the Ward identities of proper vertices for this system are obtained. The conserved charges at the quantum level are also obtained. The effective Lagrangian in configuration space for the present model is derived in the case ρ = const. Thus, the Feynman rule can be deduced immediately.