Spinning particles, braid groups and solitons

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 spinc structure. ((orig.))