El polinomio de Jones y la mecanica cuantica

TL;DR

This paper explores the connection between the Jones polynomial and quantum mechanics, focusing on the quantization of moduli spaces of flat connections and potential applications to the fractional quantum Hall effect.

Contribution

It links the Jones polynomial to quantum mechanics through the quantization of moduli spaces, specifically illustrating the Weyl quantization on a torus and suggesting applications to quantum Hall phenomena.

Findings

Quantization of the moduli space relates to the Jones polynomial.

Weyl quantization is used in the torus case.

Potential application to fractional quantum Hall effect.

Abstract

In this paper we discuss progress made in the study of the Jones polynomial from the point of view of quantum mechanics. This study reduces to the understanding of the quantization of the moduli space of flat SU(2)-connections on a surface with the Chern-Simons lagrangian. We outline some background material, then present the particular example of the torus, in which case it is known that the quantization in question is the Weyl quantization. The paper concludes with a possible application of this theory to the study of the fractional quantum Hall effect, an idea originating in the works of Moore and Read.