On the relation between the anyon and Calogero models

In order to achieve in configuration space a dimensional reduction from dim ension two to one, the lowest Landau level (LLL) projection is not sufficie nt. One has also, once in the LLL, to take the vanishing magnetic field lim it, a procedure which can be given a non ambiguous meaning by means of a lo ng distance regulator. A thermodynamical argument is proposed which support s this claim. As an illustration, the equivalence of the LLL anyon model in the vanishing magnetic field limit to the Calogero model is established. S ome general considerations in favor of an intimate connexion between anyon and Haldane statistics are also given. (C) 2001 Published by Elsevier Scien ce B.V.