Fractional dimensional Fock space and Haldane's exclusion statistics: q/p case and t−J model

The discussion of fractional dimensional Hilbert spaces in the context of Haldane exclusion statistics is extended from the case of g = 1/p for the statistical parameter to the case of rational g = q/p with q,p coprime positive integers, The corresponding statistical mechanics for a gas of such particles is constructed, This procedure is used to define the statistical mechanics for particles with irrational g. Applications to strongly correlated systems such as the Hubbard and t-J models are discussed.