Peculiarities of the spectrum of strongly correlated electrons

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Hole and spin Green's functions of the two-dimensional t-J model of the Cu-O planes are calculated in an approximation which retains the rotation symmetry in the paramagnetic state and has no presumed magnetic ordering. In this approximation Green's functions are represented by continued fractions which are interrupted by decouplings with a vertex correction determined from the constraint of zero site magnetization in the paramagnetic state. Obtained results are shown to be in good agreement with Monte Carlo and exact diagonalization data. The calculated spectra demonstrate a pseudogap and a band splitting which are similar to those observed in Bi-based cuprate perovskites.