/ 92 06 04 9 v 1 1 1 Ju n 19 92 Explicit Solution to the N - body Calogero problem USITP - 92 - 5 May 1992
نویسنده
چکیده
We solve the N-body Calogero problem, i.e. N particles in 1 dimension subject to a two-body interaction of the form 1 2 ∑ i,j[(xi − xj) + g/(xi − xj)], by constructing annihilation and creation operators of the form ai = 1 √ 2 (xi±ip̂i), where p̂i is a modified momentum operator obeying Heisenberg-type commutation relations with xi, involving explicitly permutation operators. On the other hand, Dj = i p̂j 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. ◦Institute of Theoretical Physics, CTH, S-41296 Göteborg, Sweden. †Institute of Theoretical Physics, University of Stockholm, Vanadisvägen 9, S-113 46 Stockholm, Sweden. Department of Theoretical Physics, P. N. Lebedev Physical Institute, 117924 Leninsky Prospect 53, Moscow, Russia. ◦ †Supported by the Swedish Natural Science Research Council
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