Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-01-14
Nucl.Phys. B431 (1994) 349-377
Physics
High Energy Physics
High Energy Physics - Theory
harvmac, 34 pages, HUTP-93/A037; UICHEP-TH/93-18; BUHEP-93-29
Scientific paper
10.1016/0550-3213(94)90109-0
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.
Brekke Lee
Dugan Michael J.
Imbo Tom D.
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