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

11 March 1983

journal article
Published by IOP Publishing in Journal of Physics A: General Physics

Vol. 16 (4) , 729-736
https://doi.org/10.1088/0305-4470/16/4/011

Abstract

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

Keywords

This publication has 3 references indexed in Scilit:

Published by IOP Publishing ,1981
Free actions of Z4 on S3
Duke Mathematical Journal, 1969
On the existence of a connection with curvature zero
Commentarii Mathematici Helvetici, 1958