Explicit Solution to the N-Body Calogero Problem

Abstract

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.

6 p., latex, USITP-92-5

References in corpus (1)

• Exchange Operator Formalism for Integrable Systems of Particles

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