  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.
