Comments about THETA-vacua and topology of the SU2 Yang-Mills theory

The topological properties of the configuration space in the SU2 Yang-Mills theory is discussed, consisting of all the field configurations for which the classical Hamiltonian is bounded, using a language which is familiar from the study of two- or three-dimensional spaces with a nontrivial topology. Assuming that the physically relevant configurations consist of all potentials approaching a pure gauge at spacial infinity, it is shown that all closed paths in the physical configuration space, which in the temporal gauge correspond to continuous paths connecting a field configuration Asub(i)sup(a)(x) with a gauge transform thereof, can be classified with the help of an ''angular variable'' by a winding number. This ''angular variable'' is a nonsingular, single-valued functional of the potentials, but a multivalued functional of the gauge invariants built from these. As a consequence, inequivalent representations for the canonical momenta exist which give rise to different THETA-worlds. (author)