SU(n) bundles over the configuration space of three identical particles moving on R3

The systems of three identical spinless particles moving on R3 and possessing an SU(n) gauge symmetry are studied. Three such systems are possible, corresponding to the three non-isomorphic SU(n) bundles over C3(R3), the configuration space. C3(R3) is retracted to a subcomplex which shows clearly how its homology arises. The three bundles can be realised as pull-backs of the universal bundle S7 → S4 using three non-homotopic maps C3(R3) → S4. The two non-trivial bundles admit no flat connection; they do not correspond to Bose, Fermi or parastatistics. (author)