ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Spin and statistics for topological solitons in nonlinear sigma models are studied using topological methods based on the classical configuration space. 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 πd(M). Any topological soliton α∈πd(M) determines a quotient Statn(X,α) of the group of framed braids with n strands on X, such that a framed braid determines a contractible path in the n-soliton sector of the configuration space if and only if its image in Statn(X,α) is the identity. In particular, when M=S2, as in the O(3) nonlinear sigma model with Hopf term, and α∈π2(S2) is a generator, we compute that Statn(R2,α)=Z, while Statn(S2,α)=Z2n. Thus one expects the phase exp(iθ) for interchanging two solitons of type α on S2 to satisfy the constraint θ=kπ/n, k∈Z, when n such solitons are present. © 1995 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.531304
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