IL NUOVO CIMENTO VOL. 109 B, N. 5 Maggio 1994 A New Type of Statistics of Identical Particles. R. SCIPIONI Dipartimento di Fi~ica dell'Universit& di Roma I ,,La Sapienza, Piazzale A. Moro 2, 00185 Rom~ Italia (ricevuto il 16 Agosto 1993; approvato il 10 Marzo 1994) Summary. -- The recently proposed g-uonic statistics is reconsidered from a more physical point of view; starting from a very general assumption about wave function we prove that it is the only possible generalisation of the Fermi and Bose statistics. PACS 05.90 - Other topics in statistical physics and thermodynamics. PACS 11.90 - Other topics in general field and particle theory. As is well known, in particle statistics there are two possibilities: the Bose- Einstein statistics and Fermi-Dirac one, corresponding, respectively, to the symmetric and anti-symmetric representations of the symmetric group. Recently, an interesting version of statistics of particles has been considered by Wu-Sun[1] based upon the following relations for the annihilation and creation operators: (1) a(i)at(j) - gat(j)a(i) = ~i,j, at(i)at(j) - ~at(j)at(i) = 0, [g, a(i)] = [g, at(i)] = 0, in which ~ is an operator which is both Hermitian and unitary: (2) ~t = 1, ~2 = 1. The proposal of Wu and Sun, although interesting, was not justified from a theoretical point of view. In this note starting from a very general assumption about the wave function of a generic particle, we wish to prove that the g-uonic statistics is in fact the only possible generalisation that we may conceive of the Bose and Fermi statistics. As we know from quantum mechanics, a generic particle is described by a wave function ~'(r) which is nothing but the density of probability of finding the particle in the region r, r + dr. In the successive generalisation to the relativistic theory, this function becomes