TY - JOUR T1 - Statistics in space dimension two JF - Lett. Math. Phys. 40 (1997), no. 3, 235-256 Y1 - 1997 A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta AB - 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). PB - SISSA Library UR - http://hdl.handle.net/1963/130 U1 - 12 U2 - LISNU U3 - Interdisciplinary Laboratory for Advanced Studies ER -