Boundary conditions and confinement in the gauge field theory at finite temperature

A Hamiltonian formulation of a non-Abelian gauge theory confined in a finit e domain is constructed in a generalized three-dimensional Fock-Schwinger g auge in the presence of surface terms. The dependence of the partition func tion on the boundary value of the longitudinal electric-field component, wh ich because of the Gauss law, coincides with the electric-field flow throug h an infinitesimal boundary-surface element in this gauge, is investigated. This dependence is related to the confinement-deconfinement phase transiti on. In the confinement phase, the chromoelectric current through any bounda ry element is zero, because all observable quantities are singlet w.r.t. th e remaining gauge-transformation group, i.e., color objects are unobservabl e at spatial infinity. in addition to the non-Abelian theory, a simpler exa mple of quantum electrodynamics with an external-charge density in a spheri cal domain is considered in which the effective partition function is exact ly calculable.