Plasmon spectrum of degenerated electron gas. T=0 Green function method. Detailed pedagogical derivation

TL;DR

This paper presents a straightforward Green function approach to derive the plasmon spectrum and polarization operator for electron gases in various dimensions, offering a clear pedagogical alternative to traditional methods.

Contribution

It introduces a simple, field theory-based derivation of the response function for electron gases, enhancing educational clarity in condensed matter physics.

Findings

Derived plasmon spectra for 1D, 2D, and 3D electron gases

Demonstrated the effectiveness of Green function techniques in response calculations

Provided pedagogical insights complementing standard physics courses

Abstract

Plasmon spectrum and polarization operator of 1, 2, and 3 dimensional electron gas are calculated by T=0 Green function technique. It is shown that this field theory method gives probably the simplest pedagogical derivation of the statistical problem for the response function. The explanation is complimentary to the standard courses on condensed matter and plasma physics of the level of IX volume of Landau-Lifshitz encyclopedia on theoretical physics.