1998/12/31 by Giovanni Landi
Physics and Astronomy · Mathematics · #math-ph #gr-qc #hep-th #math.MP
published as Rev.Math.Phys. 12 (2000) 1367-1390 · latex, 23 pages (one additional page). Additional material at the end of Section 2. and a reference added. Several minor additions throughout the paper
arxiv created 1999/01/05 · arxiv updated 2009/11/30
We give a unifying description of the Dirac monopole on the 2-sphere S2, of a graded monopole on a (2,2)-supersphere S2,2 and of the BPST instanton on the 4-sphere S4, by constructing a suitable global projector p via equivariant maps. This projector determines the projective module of finite type of sections of the corresponding vector bundle. The canonical connection ∇ = p ∘ d is used to compute the topological charge which is found to be equal to -1 for the three cases. The transposed projector q=pt gives the value +1 for the charges; this showing that transposition of projectors, although an isomorphism in K-theory, is not the identity map. We also study the invariance under the action of suitable Lie groups.