Gluon and Ghost Propagators at Finite Temperatures within a Dyson–Schwinger Approach

We investigate the finite-temperature structure of ghost and gluon propagators within an approach based on the rainbow truncated Dyson–Schwinger equations in the Landau gauge. The method early used for modeling quark, ghost and gluon propagators in vacuum is extended to finite temperatures. In Euclidean space, within the Matsubara imaginary time formalism the Dyson–Schwinger equation splits into a system of coupled equations for transversal and longitudinal propagatators. This system is considered within the rainbow approximation generalized to finite temperatures and solved numerically. The solutions to the ghost and gluon propagators are obtained as functions of temperature $$T$$ , Matsubara frequency $${{\Omega }_{n}}$$ and three-momentum squared $${{k}^{2}}$$ . It is found that in the vicinity of a certain value of the temperature $${{T}_{0}} \sim 150$$ MeV the longitudinal gluon propagator increases quite fastly, whereas the transversal propagator does not exhibit any irregularity. This is in qualitative agreement with the results obtained within the QCD lattice calculations in this temperature interval.