Non-invariant ground states, thermal average, and generalized fermionic statistics

We present an approach to generalized fermionic statistics which relates th e existence of a generalized statistical behaviour to non-invariant ground states. Considering the thermal average of an operator generalization of th e Heisenberg algebra, we get an occupation number which depends on the degr ee of mixing between symmetric and antisymmetric sectors of the ground stat e. A natural prescription is given for the construction of a supersymmetric statistics. We also show that the structure of the vacuum, and therefore t he statistical behaviour of the system, can be accounted for in terms of a second-order phase transition. (C) 1999 Published by Elsevier Science B.V. All rights reserved.