EXPLICIT SOLUTION TO THE N-BODY CALOGERO PROBLEM

We solve the N-body Calogero problem, i.e., N particles in one dimension subject to a two-body interaction of the form 1/2 SIGMA(i,j) [(x(i) - x(j))2 + g/(x(i) - x(j))2], by constructing annihilation and creation operators of the form a(i)-/+ = (1/square-root 2)(x(i)+/-ip(i)), where 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) = ip(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.