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The partition function of a relativistic invariant quantum field theory isexpressed by its vacuum energy calculated on a spatial manifold with onedimension compactified to a 1-sphere $S^1 (\beta)$, whose circumference $\beta$represents the inverse temperature. Explicit expressions for the usual energydensity and pressure in terms of the energy density on the partiallycompactified spatial manifold $\mathbb{R}^2 \times S^1 (\beta)$ are derived. Tomake the resulting expressions mathematically well-defined a Poissonresummation of the Matsubara sums as well as an analytic continuation in thechemical potential are required. The new approach to finite-temperature quantumfield theories is advantageous in a Hamilton formulation since it does notrequire the usual thermal averages with the density operator. Instead, thewhole finite-temperature behaviour is encoded in the vacuum wave functional onthe spatial manifold $\mathbb{R}^2 \times S^1 (\beta)$. We illustrate thisapproach by calculating the pressure of a relativistic Bose and Fermi gas andreproduce the known results obtained from the usual grand canonical ensemble.As a first non-trivial application we calculate the pressure of Yang-Millstheory as function of the temperature in a quasi-particle approximationmotivated by variational calculations in Coulomb gauge.

Hamiltonian finite-temperature quantum field theory from its vacuum on partially compactified space