Probabilities and path-integral realization of exclusion statistics

A microscopic formulation of Haldaneʹs exclusions statistics is given in terms of a priori occupation probabilities of states. It is shown that negative probabilities are always necessary to reproduce fractional statistics. Based on this formulation, a path-integral realization for systems with exclusion statistics is derived. This has the advantage of being generalizable to interacting systems, and can be used as the starting point for further generalizations of statistics. As a byproduct, the vanishing of the heat capacity at zero temperature for exclusion statistics systems is proved.