Dynamical equation determining plasmon energy spectrum in a metallic slab

Abstract

On the basis of general principles of electrodynamics and quantum theory we have elaborated the quantum field theory of plasmons in the plane metallic slab with a finite thickness by applying the functional integral technique. A hermitian scalar field φ was used to describe the collective oscillations of the interacting electron gas in the slab and the effective action functional of the system was established in the harmonic approximation. The fluctuations of this scalar field φ around the background one φ0 corresponding to the extreme value of the effective action functional are described by the fluctuation field ζ generating the plasmons. The dynamical equation for this fluctuation field was derived. The solution of the dynamical equation would determine the plasmon energy spectrum.