Dispersion in a relativistic degenerate electron gas

Abstract

Relativistic effects on dispersion in a degenerate electron gas are discussed by comparing known response functions derived relativistically (by Jancovici) and nonrelativistically (by Lindhard). The main distinguishing feature is one-photon pair creation, which leads to logarithmic singularities in the response functions. Dispersion curves for longitudinal waves have a similar tongue-like appearance in the relativistic and nonrelativistic case, with the main relativistic effects being on the Fermi speed and the cutoff frequency. For transverse waves the nonrelativistic treatment has a nonphysical feature near the cutoff frequency for large Fermi momenta, and this is attributed to an incorrect treatment of the electron spin. We find (with two important provisos) that one-photon pair creation is allowed in superdense plasmas, implying relatively strong coupling between transverse waves and pair creation.

17 pages, 9 figures. Submitted to Physical Review E

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• The photo-neutrino process in astrophysical systems
• Differential Neutrino Rates and Emissivities from the Plasma Process in Astrophysical Systems
• Relativistic quantum plasma dispersion functions
• Bremsstrahlung neutrinos from electron-electron scattering in a relativistic degenerate electron plasma
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• Plasmon excitations in homogeneous neutron star matter
• Plasmons in strong superconductors
• Finite-temperature electromagnetic responses of relativistic electrons
• Electromagnetic propagation in a relativistic electron gas at finite temperatures
• Negative refraction in the relativistic electron gas