Dell'Antonio G.F., Figari R., Teta A.
Statistics in Space Dimension Two
(58K, TeX)
ABSTRACT. We construct as a selfadjoint operator the Schroedinger hamiltonian for a
system of $N$ identical particles on a plane, obeying the statistics defined
by a representation $\pi_1$ of the braid group. We use quadratic forms and
potential theory, and give details only for the free case; standard
arguments provide the extension of our approach to the case of potentials
which are small in the sense of forms with respect to the laplacian.
We also comment on the relation between the analysis given here and other
approaches to the problem, and also on the connection with the description of a
quantum particle on a plane under the influence of a shielded magnetic field
(Aharanov-Bohm effect).