Abstract
The thermodynamics of $SU(2)$ Yang-Mills theory in the covariant variational
approach is studied by relating the free action density in the background of a
non-trivial Polyakov loop to the pressure of the gluon plasma. Subtleties in
this identification due to the presence of massless gauge modes are discussed
in detail, and the correct subtraction of the vacuum contribution in the
pressure is argued for. The Poisson resummed expression for the pressure can be
evaluated analytically in limiting cases, and shows both a smooth limit at $T
0$ and the correct Stefan-Boltzmann limit at $T ınfty$. Using the
numerical $T=0$ solutions for the ghost and gluon propagators in the covariant
variational approach as input, the pressure, energy density and interaction
strength are calculated and compared to lattice data.
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