We give the analytic expression of the next-to-leading order contribution to the longitudinal gluons energy in high-temperature quantum chromodynamic using the real-time formalism of finite-temperature quantum field theory. We also give the expressions of the effective propagators and vertex functions.
Properties of a two-level atom coupled to the quantized electromagnetic field at finite temperature are determined. The analysis is based on a new method (inspired by quantum electrodynamics) of describing qubits, developed previously at zero temperature. In this paper, we make a generalization to finite temperature by introducing the Matsubara formalism and the temperature propagators. We analyze the spectral properties of different types of propagators and we derive a direct connection between the temperature propagators and the real time propagators. To show the effectiveness of this method, we calculate the temperature dependence of the polarizability of a two-level atom in the lowest order of perturbation theory and we predict an unexpected sharpening of the resonance. The whole discussion is carried out without the rotating wave approximation.
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