  Properties of pure gauge theories in thermal equilibrium as calculated via
standard functional integral treatments are mathematically identical to ground
state properties of a theory with spatially-periodic boundary conditions
imposed on the gauge fields. Such a theory has states that have no analog in a
theory in which only physical observables associated with gauge-invariant
operators are required to be periodic, rather than the gauge fields themselves;
these states are in topological sectors that do not exist in the unconstrained
theory. The topology arises because the boundary conditions in the functional
integral are gauge invariant on a cylinder but not in the unconstrained theory.
