  We consider finite temperature SU(2) gauge theory in the continuum
formulation, which necessitates the choice of a gauge fixing. Choosing the
Landau gauge, the existing gauge copies are taken into account by means of the
Gribov-Zwanziger (GZ) quantization scheme, which entails the introduction of a
dynamical mass scale (Gribov mass) directly influencing the Green functions of
the theory. Here, we determine simultaneously the Polyakov loop (vacuum
expectation value) and Gribov mass in terms of temperature, by minimizing the
vacuum energy w.r.t. the Polyakov loop parameter and solving the Gribov gap
equation. Inspired by the Casimir energy-style of computation, we illustrate
the usage of Zeta function regularization in finite temperature calculations.
Our main result is that the Gribov mass directly feels the deconfinement
transition, visible from a cusp occurring at the same temperature where the
Polyakov loop becomes nonzero. In this exploratory work we mainly restrict
ourselves to the original Gribov-Zwanziger quantization procedure in order to
illustrate the approach and the potential direct link between the vacuum
structure of the theory (dynamical mass scales) and (de)confinement. We also
present a first look at the critical temperature obtained from the Refined
Gribov-Zwanziger approach. Finally, a particular problem for the pressure at
low temperatures is reported.
