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A variational treatment of the Gutzwiller - renormalized t-J Hamiltoniancombined with the mean-field (MF) approximation is proposed, with asimultaneous inclusion of additional consistency conditions. Those conditionsguarantee that the averages calculated variationally represent true mean-fieldexpectation values. This is not ensured a priori when the effective Hamiltoniancontains renormalization factors which depend on the mean-field averages. Acomparison with previous mean-field treatments is made for both superconducting(d-RVB) and normal states and encompasses calculations of both thesuperconducting gap and the renormalized hopping amplitudes, as well as theelectronic structure. The $C_{4v}$-symmetry breaking in the normal phase - thePomeranchuk instability (PI) - is also analyzed.

A consistent statistical treatment of the renormalized mean-field t-J model