Uniform quantized electron gas: Radiation corrections

TL;DR

This paper investigates how radiation effects modify the correlation functions and energies of a zero-temperature electron gas using path integral formalism, extending previous electrostatic studies to include radiation corrections.

Contribution

It introduces a quantum statistical mechanical approach to incorporate radiation effects into the correlation analysis of the electron gas, providing new insights into dielectric properties and energy contributions.

Findings

Radiation effects influence correlation functions and energies.

Transverse energy contributions are small but significant at high densities.

Dielectric constants are derived from induced correlation functions.

Abstract

In this paper we analyze how radiation effects influence the correlation functions, the excess energy, and in turn the electron correlation energy of the quantized electron gas at temperature $T=0$. To that aim we resort to a statistical mechanical description of the quantum problem of electron correlations, based on the path integral formalism. In previous works we studied and found accurate results for the usual situation with the electrostatic Coulomb interaction. Here the additional problem with radiation is taken into account. This is facilitated by the equivalence to a dielectric fluid for which correlation functions for dipolar moments are established. From these functions follows the usual density-density (or charge-charge) correlation function needed for the longitudinal electrostatic problem, and in addition the one needed for the transverse radiation problem. While electrostatic excess energy is negative, the transverse one is positive. This quantity is small and decreases rapidly for decreasing densities. However, for high densities it approaches the electrostatic contribution, eventually becoming even larger. The part of the transverse energy from induced correlations turns out to be very small. Also, the non-local longitudinal and transverse dielectric constants of the electron gas are identified from the induced correlation functions.