PHYSICAL REVIEW D, cilt.63, sa.8, 2001 (SCI-Expanded)
We demonstrate by explicit construction that while the untwisted Harrington-Shepard caloron A(mu) is manifestly periodic in Euclidean time, with a period beta =1/T, when transformed to the Weyl (A(0)=0) gauge, the caloron gauge field A(i) is periodic only up to a large gauge transformation, with the winding number equal to the caloron's topological charge. This helps clarify the tunneling interpretation of these solutions, and their relation to Chem-Simons numbers and winding numbers.