QCD Propagators at non-vanishing temperatures

We investigate the behaviour of the gluon and ghost propagators, especially their infrared properties, at non-vanishing temperatures. To this end we solve their Dyson-Schwinger equations on a torus and find an infrared enhanced ghost propagator and an infrared vanishing gluon propagator. Lattice simulations provide evidence that zero-flavour QCD undergoes a ”deconfining” phase transition at some critical temperature. The properties of the gluon and the ghost propagator at finite temperature can provide insights into the mechanisms of this phase transition and they are related to the issue of confinement and deconfinement. We study the Dyson-Schwinger equations (DSEs) of these propagators in Landau gauge for which a well understood truncation scheme at zero temperature is available [1]. The infrared behaviour of the gluon and ghost propagators can be determined analytically and we obtain power-laws. This is consistent with the Kugo-Ojima confinement picture for Landau gauge, which requires the ghost propagator to diverge stronger than a free propagator at zero momentum. On the other hand the gluon propagator is infrared suppressed (Dμν(k → 0) = 0). Thus it violates positivity and the gluons are removed from the physical spectrum [2]. Since this infrared singular structure is expected to persist for non-vanishing temperatures a continuum based method for studying the deconfinement phase transition is desirable. At non-vanishing temperatures the analytical determination of the infrared behaviour has not been achieved yet, thus we need an infrared regulator. A possible one is to compactify space-time to a four dimensional torus by imposing periodic boundary conditions on the fields. This has been done already at zero temperature [3]. The truncation scheme at zero temperature described in [3] is extended to finite temperatures in the Matsubara-Formalism (imaginary time formalism) for thermodynamical equilibrium. The DSEs in pure Yang-Mills-Theory for the gluon and the ghost propagator are considered. Since the heat bath defines a prefered reference frame, the full gluon-propagator in Landau gauge now depends on two independent transverse tensor structures, a heat-bath transverse and longitudinal part, leading to the following decomposition [4]: