The Fourier transforms of the thermal two-time single-particle Green functions may be expressed as matrix elements of the resolvent of the Liouville operator, in an abstract Hilbert space. This abstract Hilbert space (the "superspace") contains elements f, g, etc. which are products of an odd number of fermion creation and/or annihilation operators. These operators may also be expressed as linear combinations of a set of stepping operators Φ = fig, where I is the projection operator for the vacuum in the ordinary Fock space. The Judd operators are stepping operators which step between many-particle states which usually differ in particle number. In the calculation of the single-particle Green function, only those single-particle Judd operators which step between states differing by one electron are relevant. The Judd operators obey a Lie algebra analogous to the angular momentum stepping operators L_±. The single-site and two-site Hubbard model for arvitrary electron density are solved exactly using the Judd operator formalism. The correlation functions are evaluated as functions of chemical potential, temperature and t/U, where t is the hopping energy and U is the intasite Coulomb energy. / Ph. D.