Topological Aspects of Spin and Statistics in Nonlinear Sigma Models

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dc.creatorBaez, John
dc.creatorOdy, Micheal
dc.creatorRichter, William
dc.date1992-08-07
dc.date.accessioned2026-07-07T11:34:15Z
dc.date.available2026-07-07T11:34:15Z
dc.descriptionWe 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 manifold $M$ as target space, topological solitons are given by elements of $pi_d(M)$. Any topological soliton $α\in π_d(M)$ determines a quotient $\Stat_n(X,α)$ of the group of framed braids on $X$, such that choices of allowed statistics for solitons of type $α$ are given by unitary representations of $\Stat_n(X,α)$ when $n$ solitons are present. In particular, when $M = S^2$, as in the $O(3)$ nonlinear sigma model with Hopf term, and $α\in π_2(S^2)$ is a generator, we compute that $\Stat_n(\R^2,α) = \Z$, while $\Stat_n(S^2,α) = \Z_{2n}$. It follows that phase $\exp(iθ)$ for interchanging two solitons of type $α$ on $S^2$ must satisfy the constraint $θ= kπ/n$, $k \in \Z$, when $n$ such solitons are present.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/cond-mat/9208005
dc.identifierhttp://arxiv.org/abs/cond-mat/9208005
dc.identifierJ.Math.Phys.36:247-257,1995
dc.identifierdoi:10.1063/1.531304
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/198183
dc.subjectCondensed Matter
dc.titleTopological Aspects of Spin and Statistics in Nonlinear Sigma Models
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