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Statistics in Space Dimension Two

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Abstract

We construct as a selfadjoint operator the Schrödinger Hamiltonian for a system of N identical particles on a plane, obeying the statistics defined by a representation π1 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).

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Authors
  1. GIANFAUSTO Dell'Antonio
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  2. RODOLFO Figari
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  3. ALESSANDRO Teta
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Dell'Antonio, G., Figari, R. & Teta, A. Statistics in Space Dimension Two. Letters in Mathematical Physics 40, 235–256 (1997). https://doi.org/10.1023/A:1007361832622

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  • DOI: https://doi.org/10.1023/A:1007361832622

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