  The partition function of a relativistic invariant quantum field theory is
expressed by its vacuum energy calculated on a spatial manifold with one
dimension compactified to a 1-sphere $S^1 (\beta)$, whose circumference $\beta$
represents the inverse temperature. Explicit expressions for the usual energy
density and pressure in terms of the energy density on the partially
compactified spatial manifold $\mathbb{R}^2 \times S^1 (\beta)$ are derived. To
make the resulting expressions mathematically well-defined a Poisson
resummation of the Matsubara sums as well as an analytic continuation in the
chemical potential are required. The new approach to finite-temperature quantum
field theories is advantageous in a Hamilton formulation since it does not
require the usual thermal averages with the density operator. Instead, the
whole finite-temperature behaviour is encoded in the vacuum wave functional on
the spatial manifold $\mathbb{R}^2 \times S^1 (\beta)$. We illustrate this
approach by calculating the pressure of a relativistic Bose and Fermi gas and
reproduce the known results obtained from the usual grand canonical ensemble.
As a first non-trivial application we calculate the pressure of Yang-Mills
theory as function of the temperature in a quasi-particle approximation
motivated by variational calculations in Coulomb gauge.
