THE SPIN STATISTICS CONNECTION FROM HOMOLOGY GROUPS OF CONFIGURATION SPACE AND AN ANYON WESS-ZUMINO TERM

The first and second homology groups H(i) for configuration spaces of framed two-dimensional particles and antiparticles, with annihilation included, are computed when up to two particles and an antiparticle are present. The set of "frames" considered are S2, SO(2) and SO(3). It is found that the H-1 groups are those of the "frames" and are generated by a cycle corresponding to a 2pi frame rotation. This same cycle is homologous to the exchange path-the spin-statistics theorem. Furthermore for the frame space SO(2), H-2 contains a Z subgroup which implies the existence of a nontrivial Wess-Zumino term. A rotationally and translationally invariant, topologically nontrivial Wess-Zumino term for a pair of anyons and an antianyon is exhibited for this case.