Gerald Goldin
Predicting Nonabelian Anyons
Nonabelian anyons are conjectured particles or excitations in two-dimensional space, whose "exchange statistics" satisfy unitary representations of the braid group of dimension greater than one. Their first prediction came in 1985 from Menikoff, Sharp, and myself, in published research whose citation researchers in the field still systematically omit. Recently nonabelian anyons have attracted considerable attention in the field of quantum computing, and experimental results have ensued. In this talk, I will outline how their prediction followed from classifying the unitary representations of a certain local symmetry group: the natural semi-direct product of a group of scalar functions with a group of diffeomorphisms of physical space. For fundamental reasons, this group serves as a universal kinematical group for quantum mechanics. Our development made clear how the topology of configuration space enters inevitably into quantum mechanics, resolving some earlier controversies about "multivalued wave functions". If time permits, I will compare and contrast this approach with conventional Schrödinger and Heisenberg quantization schemes, and mention some of my ongoing research directions.
