Dispersion in a magnetized, quantum electron gas was first discussed in the nonrelativistic case in the 1960s and 1970s [24, 15, 7, 6, 2]. Extension to the relativistic case, with one early exception , was carried out mainly in the 1980s [3, 5, 13, 8] and continues to the present [14, 22, 11]. An exact expression for the linear response tensor includes the following quantum effects: degeneracy, the quantization of the Landau states, the spin, the quantum recoil and dispersion associated with one-photon pair creation. It involves sums over two sets of quantum numbers, denoted q=ε,n, pz, s and q′=ε′, n′, p′z, s′ here. This leads to a cumbersome form, and only a few special cases, notably parallel propagation, have been explored in any detail.
Occupation Number Logarithmic Singularity Pair Creation Degenerate Distribution Landau State
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N.N. Bogoliubov, D.V. Shirkov, The Theory of Quantized Fields (Interscience, New York, 1959)Google Scholar