Na. Sveshnikov et Eg. Timoshenko, Boundary conditions and confinement in the gauge field theory at finite temperature, THEOR MATH, 117(2), 1998, pp. 1274-1285
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.