We argue that, in a guage field theory defined in a finite-volume box, some set of constraints should be imposed on the surface fields in order to get the proper equations of motion of the fields on the surface. For the pure SU(2) gauge theory we present four such sets. Each one of them predicts a different consistent theory, in which the ambiguity in $A_0$ is removed, and all the constraints become an identity of the theory. In each one of these theories some of the total electric and/or magnetic charges vanish identically. We realize these constraints and "Gauss's law" (${\dot{\pi }}_0^a=0\mathrm{}$) in a remodified axial gauge: ${\partial }_3{A}_3=0\mathrm{}$. Such an analysis and procedure can be done similarly for other gauge theories and/or other gauges.

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