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c for the condensation of s-wave and dγ-wave Cooper pairs of auxiliary fermions, which are often called spinons, are reduced by repulsive U′ and U″, respectively, and they are enhanced by attractive U′ and U″. If we consider seriously the restriction of the Hilbert space, we had better take infinitely large repulsive on-site U′ and we should treat H̄′ seriously and properly. When U′ is small, auxiliary particles are itinerant in the MF theory. However, they must be localized in the limit of infinitely large repulsive U′ when the average number of auxiliary particles is just one per site, as electrons are localized in the just half-filled Hubbard model with indefinitely large on-site repulsion U; only pair excitations can be itinerant such as those of auxiliary particles in the auxiliary-particle model and those of electrons in the Hubbard model.
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When we take the other statistics different from those of the slave-boson t-J model, fermionic e, and bosonic c particles, results in the MF approximation for such a model are totally different from those for the slave-boson t-J model. One of the most remarkable differences is that the volumes of the Fermi surface are totally different between the two models. This is other evidence that the MF approximation for the auxiliary-particle models, including the slave boson t-J model, is irrelevant to describe dynamics of electrons in the original t-J model.
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