Anyons in Geometric Models of Matter
Mathematical Physics
2017-08-02 v2 Geometric Topology
math.MP
Abstract
We show that the "geometric models of matter" approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold singularities along embedded 2-dimensional surfaces. The anyon states arise through the braid representation of surface braids wrapped around the orbifold singularities, coming from multisections of the orbifold normal bundle of the embedded surface. We show that the resulting braid representations can give rise to a universal quantum computer.
Keywords
Cite
@article{arxiv.1611.04047,
title = {Anyons in Geometric Models of Matter},
author = {Michael Atiyah and Matilde Marcolli},
journal= {arXiv preprint arXiv:1611.04047},
year = {2017}
}
Comments
22 pages LaTeX