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Abstract
Abstract In quantum gauge theory, when a particular direction xa is compactified to a circle, the energy of the vacuum Veff becomes dependent on a constant value AμaC of the gauge potential. The parameter C is a periodic variable, and the vacuum energy typically has a local minimum at C = 0. Circular topology implies, of course, periodic boundary conditions in xa. When the boundary conditions around the circle are changed to, say, Dirichlet ones, the variable C becomes noncompact, and it turns out that the vacuum energy has no global minimum. We interpret this to mean that quantum gauge theories with Dirichlet or similar boundary conditions on actual boundaries are not well defined.
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