Covariant Wigner function approach for relativistic quantum plasmas

In this paper a general formalism for the treatment of relativistic quantum plasmas is given. It is manifestly covariant and rests on the use of a (covariant) relativistic Wigner function. Here it is applied to the particular case where spin effects are neglected (in most astrophysical applications this is a good approximation): a relativistic quantum Bogoliubov-Born-Green-Kirkwood-Yvan (BBGKY) hierarchy is given. The Vlasov approximation (Hartree approximation) is then considered and dispersion relations are obtained. Limiting cases (relativistic nonquantum high-temperature plasma and relativistic degenerate zero-temperature plasma) obtained previously by other authors are found anew. Finally, the formalism given appears to be much simpler and physically more transparent than many-body techniques used elsewhere