Speaker
Joost Slingerland
(National University of Ireland Maynooth)
Description
I will give an introduction to the "loop braid group". This
group
governs the topological exchange properties of ring shaped
"particles"
in three dimensional space. It plays a role similar to that of
the
braid group in 2 spatial dimensions. Loops can perform a
number of
nontrivial exchange motions including simple exchanges like
those of
point particles and "leapfrogging" like smoke rings.
I will introduce the concept of a local representation of the
loop
braid group; in such a representation, each ring has an
internal
Hilbert space and exchange motions act only on the internal
Hilbert
spaces of the rings that are involved in the motion. Examples
of such
local representations come from gauge theories and are
closely related
to the anyons that arise in toric code models, or discrete
gauge
theories. I will argue that, subject to an additional condition,
all
local representations of the loop braid group are of this type.
