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• W2007362807 endingPage "377" @default.
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• W2007362807 abstract "We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of $M$ which is the relevant object for structureless particles. In particular, we compute these generalized braid groups for particles with an internal spin degree of freedom on an arbitrary $M$. A study of their unitary representations allows us to determine the available spectrum of spin and statistics on $M$ in a certain class of quantum theories. One interesting result is that half-integral spin quantizations are obtained on certain manifolds having an obstruction to an ordinary spin structure. We also compare our results to corresponding ones for topological solitons in $O(d+1)$-invariant nonlinear sigma models in $(d+1)$-dimensions, generalizing recent studies in two spatial dimensions. Finally, we prove that there exists a general scalar quantum theory yielding half-integral spin for particles (or $O(d+1)$ solitons) on a closed, orientable manifold $M$ if and only if $M$ possesses a ${rm spin}_c$ structure." @default.
• W2007362807 created "2016-06-24" @default.
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• W2007362807 date "1994-12-01" @default.
• W2007362807 modified "2023-09-27" @default.
• W2007362807 title "Spinning particles, braid groups and solitons" @default.
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• W2007362807 doi "https://doi.org/10.1016/0550-3213(94)90109-0" @default.
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