Linking Numbers, Spin, and Statistics of Solitons

Frank Wilczek; A. Zee

doi:10.1103/PhysRevLett.51.2250

Linking Numbers, Spin, and Statistics of Solitons

Frank Wilczek and A. Zee

Phys. Rev. Lett. 51, 2250 – Published 19 December 1983

Abstract

The spin and statistics of solitons in the (2+1)- and (3+1)-dimensional nonlinear $σ$ models is considered. For the (2+1)-dimensional case, there is the possibility of fractional spin and exotic statistics; for 3+1 dimensions the usual spin-statistics relation is demonstrated. The linking-number interpretation of the Hopf invariant and the use of suspension considerably simplify the analysis.

Received 24 October 1983

DOI:https://doi.org/10.1103/PhysRevLett.51.2250

Authors & Affiliations

Frank Wilczek

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106

A. Zee^*

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, and Department of Physics, University of Washington, Seattle, Washington 98195