Almost periodic Schrödinger operators. IV. The Maryland model: Barry Simon. Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 61 KB
• Volume: 158
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(84)90134-9

✦ Synopsis

The fluctuations of various parameters of the relativistic quantum plasma are studied with the use of the covariant Wigner function techniques. The fluctuations of the covariant Wigner function of the ideal Fermi gas at thermal equilibrium are calculated. The result is a function of the one particle Wigner function and the anticommutator of the Dirac fields only. As a consequence second-order correlation functions of the four-current and the momentum-energy tensor are obtained and analyzed. On the basis of the fluctuation-dissipation theorem, the polarization tensors at tirst order in e* of the magnetized and the nonmagnetized electron gas are derived from the four-current fluctuations of the ideal plasma. Expressions are given for the magnetized vacuum polarization in two representations, integral and discrete sums over Landau levels, for arbitrary values of the photon four-momentum. The dispersion relations of the magnetized gas are studied in the limit of low frequencies and wavenumbers. It is shown that owing to relativistic quantum effects, the characteristic frequencies of the plasma modes (plasma and Larmor frequencies) split into effective transverse and longitudinal frequencies. The existence of an acoustic mode (zero sound) for the one-component plasma is also shown.