Topological aspects of spin and statistics in nonlinear sigma models

Publisher Website
Google Scholar
Abstract
We study the purely topological restrictions on allowed spin and statistics of topological solitons in nonlinear sigma models. Taking as space the connected d-manifold X, and considering nonlinear sigma models with the connected man- ifold M as target space, topological solitons are given by elements ofd(M). Any topological soliton � ∈ �d(M) determines a quotient Statn(X,�) of the group of framed braids on X, such that choices of allowed statistics for soli- tons of typeare given by unitary representations of Statn(X,�) when n solitons are present. In particular, when M = S2, as in the O(3) nonlinear sigma model with Hopf term, and � ∈ �2(S2) is a generator, we compute that Statn(R2,�) = Z, while Statn(S2,�) = Z2n. It follows that phase exp(i�) for interchanging two solitons of typeon S2 must satisfy the constraint � = k�/n, k ∈ Z, when n such solitons are present.
All Related Versions

This publication has 28 references indexed in Scilit: