  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
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