The Spin-Statistics Connection from Homology Groups of Configuration Space and an Anyon Wess-Zumino Term

Balachandran, A. P. and McGlinn, W. D. and O'Raifeartaigh, L. and Sen, S. and Sorkin, R. D. (1992) The Spin-Statistics Connection from Homology Groups of Configuration Space and an Anyon Wess-Zumino Term. (Preprint)

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Abstract

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 S^2, 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 2π 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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 14:12
Last Modified: 19 Jul 2018 10:30
URI: http://dair.dias.ie/id/eprint/729

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