Many-Anyons Wavefunction, State Capacity and Gentile Statistics

Abstract

The many-anyons wavefunction is constructed via the superposition of all the permutations on the direct product of single anyon states and its interchange properties are examined. The phase of permutation is not a representation but the word metric of the permutation group . Amazingly the interchange phase yields a finite capacity of one quantum state interpolating between Fermion and Boson and the mutual exchange phase has no explicit effect on statistics. Finite capacity of quantum state is defined as Gentile statistics and it is different from the fractional exclusion statistics. Some discussion on the general model is also given.