Explicit Solution to the N-Body Calogero Problem

Details Explicit Solution to the N-Body Calogero Problem Explicit Solution to the N-Body Calogero Problem

1992-06-11

arxiv.org/abs/hep-th/9206049v1

Phys.Lett. B286 (1992) 109-111

Physics

High Energy Physics

High Energy Physics - Theory

6 p., latex, USITP-92-5

Scientific paper

10.1016/0370-2693(92)90166-2

We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$, by constructing annihilation and creation operators of the form $ a_i^\mp =\frac 1 {\sqrt 2} (x _i \pm i\hat{p}_i )$, where $\hat{p}_i$ is a modified momentum operator obeying %!!!!!!! Heisenberg-type commutation relations with $x_i$, involving explicitly permutation operators. On the other hand, $ D_j =i\,\hat{p}_j$ can be interpreted as a covariant derivative corresponding to a flat connection. The relation to fractional statistics in 1+1 dimensions and anyons in a strong magnetic field is briefly discussed.

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