Screening length, dispersion relations and quark potential in thermo field dynamics

Abstract

The screening length in a quark-gluon plasma, the dispersion relations of thermal gluon self-energy and the quark potential at high temperature are studied within thermo field dynamics framework. By calculation of the real and imaginary parts, of the gluon self-energy in one-loop order in thermo field dynamics, we obtain an expression for the screening length in a quark-gluon plasma and the dispersion relation between the real and imaginary parts. At high temperature, using photon exchange between electron-positron in a skeleton expansion and ladder approximation, the screened Coulomb potential is obtained, and using one-gluon and two-gluon exchange between a quark-antiquark, we get an expression for the screened quark potential up to $O(g amplitudes of generic process taking place in a many body system in equilibrium at temperature T. The relationship of the scattering and decay amplitudes as calculated in Thermo Field Dynamics to the conventional techniques is established. It is shown that in many cases the calculations are relatively easy in TFD.