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Dispersion in a relativistic degenerate electron gas

J. McOrist·D. B. Melrose·J. I. Weise
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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.

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J. McOrist, D. B. Melrose, J. I. Weise. 2006-03-27. Dispersion in a relativistic degenerate electron gas. https://doi.org/10.1017/s0022377806004806

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