Dispersion in a Relativistic Quantum Electron Gas. II. Thermal Distributions

The dispersion functions which appear when the response of a non-degenerate thermal electron gas is treated using a relativistic quantum theory are shown to be the same as the functions which appear in the non-quantum limit. These functions are evaluated at two speeds V1 and V2 which in the non-quantum limit reduce to the phase speed ca/I k I. It is shown that the effects of partial degeneracy may be included by expanding about the non-degenerate limit, and the expansion of the response functions is given explicitly. It is also pointed out that thermal corrections to the completely degenerate limit may be included using a standard technique and the lowest order corrections are given.