Topological exchange statistics in one dimension

In two dimensions, the topological approach to exchange statistics predicts the existence of anyons obeying statistics given by the braid group. However, in one dimension the topological approach is ambiguous because particles cannot exchange without coincidence and scattering. I will review the topological approach and show how old controversies can be resolved using orbifolds (roughly, manifolds with symmetry) to describe configuration space for one-dimensional systems. Using orbifolds also predicts new topological physics, including possibilities for “traid group” statistics when there are three-body interactions in one dimension and non-abelian statistics for indistinguishable particles on a ring.

*Detailed information about the seminar refer to the email.