Spinning particles, braid groups and solitons

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