Functional integral method in quantum

Abstract

In the present work the quantum theory of plasmon was established on the basis of the fundamental principles of quantum physics applied to the electron gas in metal and with the use of the functional integral method. By means of the celebrated Hubbard-Stratonovich transformation, from the generating functional of the electron gas it follows that of a scalar field whose destruction and creation operators are those of plasmons. In the case of the electron gas in a homogeneous unbounded metal at zero absolute temperature T = 0, the Lagrangian of the scalar field describing the plasmon has the same form as that of the relativistic Klein-Gordon scalar field. The presented reasonnings and calculations can be extended to study electron gas in nanostructures.