Tensor categories and quantization for the quantum Hall effect

Abstract: The aim of this talk is to show that quantization of the Hall conductance in the infinite plane geometry follows from the finiteness of the number of the superselection sectors of microscopic quantum lattice systems. These are equivalence classes of certain representations of the algebra of observables, which correspond physically to types of quasi-particle excitations. I will review aspects of this representation theory, show how it is naturally described in terms of a certain category, and explain how the Hall conductance appears within this framework. This is joint work with M. Corbelli, M. Fraas and Y. Ogata.

mathematical physics

Audience: researchers in the discipline

One world IAMP mathematical physics seminar

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