9 - Finite temperatures

Summary

Finite-temperature quantum field theories at thermodynamic equilibrium are naturally described by Euclidean path integrals. The time-variable in this approach is compactified and varies between 0 and the inverse temperature 1/T. Periodic boundary conditions are imposed on Bose fields, while antiperiodic ones are imposed on Fermi fields in order to reproduce the standard Bose or Fermi statistics, respectively.

The lattice formulation of QCD at finite temperature is especially simple, since the Euclidean lattice has a finite extent in the temporal direction. The Wilson criterion of confinement is not applicable at finite temperatures and is replaced by another one based on the thermal Wilson lines passing through the lattice in the temporal direction. They are closed owing to the periodic boundary condition for the gauge field.

When the temperature increases, QCD undergoes [Pol78, Sus79] a deconfining phase transition which is associated with a liberation of quarks. At low temperatures below the phase transition, thermodynamical properties of the hadron matter are well described by a gas of noninteracting hadrons while at high temperatures above the phase transition these are well described by an ideal gas of quarks and gluons.

The situation with the deconfining phase transition becomes less definite when the effects of virtual quarks are taken into account. The deconfining phase transition makes strict sense only for large values of the quark mass. For light quarks, a phase transition associated with the chiral symmetry restoration at high temperatures occurs with increasing temperature. It makes strict sense only for massless quarks.