Abstract
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 , whose circumference 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 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 behavior is encoded in the vacuum wave functional on the spatial manifold . 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 nontrivial application we calculate the pressure of Yang-Mills theory as a function of the temperature in a quasiparticle approximation motivated by variational calculations in Coulomb gauge.
- Received 1 July 2016
DOI:https://doi.org/10.1103/PhysRevD.94.045016
© 2016 American Physical Society