Background field method in thermo field dynamics for wave propagation in unmagnetized spinor QED plasmas

Abstract

In this paper, we propose a relativistic quantum many-body theory for the collective modes in spinor quantum electrodynamic plasma. Different from the usual quantization scheme, we use the self-consistency nontrivial background field method in the framework of thermo field dynamics, in which the resulting quanta are temperature-dependent particles instead of the observable ones such as electrons, positrons, and photons. The theory provides a general scheme for many-body physics, which overcomes the disadvantages of random phase, Hartree–Fock, or other equivalent mean-field approximations. The essential point for our theory is to exactly evaluate the background fields. In this paper, we propose a general and efficient method to determine them, which we name as the “classical limit method” for convenience. To demonstrate how to apply the theory, we discuss the collective modes in unmagnetized electron–positron plasma, in both the low-energy and high-energy limits. It yields the well-known dispersion relations of longitudinal and transverse modes for non-relativistic degenerate plasmas, at zero and nonzero temperature. Furthermore, it gives the additional relativistic and vacuum fluctuation corrections, including increasing mass, decreasing effective charge, finite light velocity influence on the dispersion relation, and virtual charge redistribution. The last effect is reported for the first time.