Quantum field theory of interacting plasmon–photon system

Van Hieu Nguyen and Bich Ha Nguyen

Abstract

In the framework of functional integral approach, quantum theory of interacting plasmon–photon system was constructed on the basis of general postulates (axioms) called also first principles of electrodynamics and quantum theory of many-body systems. Since plasmons are complex quasiparticles appearing as the resonances in plasma oscillations of the electron gas in solids, we start from the general expression of total action functional of interacting system consisting of electron gas and electromagnetic field. The collective oscillations of electron gas are characterized by a real scalar field (x) called the collective oscillation field. In the harmonic approximation the collective oscillations behave like the small fluctuations around a background field ₀(x). The difference between (x) and ₀(x) is called the fluctuation field ζ(x). In the case of a homogeneous and isotropic electron gas the fluctuation field ζ(x) is a linear functional of another real scalar field σ(x) satisfying the wave equation similar to the Klein–Gordon equation in relativistic quantum field theory. The quanta of corresponding Hermitian scalar field  are called plasmons. The real scalar field σ(x) is called plasmonic field. The total action functional of the interacting system of plasmonic and electromagnetic field was derived