Gauge vacuums and the conformal group

Abstract

Recent discussions on the degeneracy of classical gauge vacuums assume that spacelike hypersurfaces in an (n + 1) -dimensional space-time have the topology of n-dimensional spheres. We point out a connection between this assumption and the requirement that the conformal group acts properly as a group of transformations on space-time. The latter is possible only if the Minkowski space M/sup n/ is enlarged to a compact manifold M/sup n/ by the addition of suitable points at infinity. Spacelike hypersurfaces in M/sup n/ do indeed have the topology of S/sup n/.