magnetic Brillouin zone boundary [@bmui]. This region corresponds to the bottom of the band . Moreover, if one takes into account the direct oxygen-oxygen hopping, finite temperature and a more complicated form for a small polaron wave function, then $\Omega _{{\bf k}}$ reproduces the experimentally observed extended saddle point which is directed along the line $(0,\pi
)-(0,0)$ [@barVan]. Therefore it seems important to clear up if the quasiparticle band reproduces the peculiarities of $\Omega 
_{{\bf k}}$ dispersion. Below we study this question for the simplest variant of the model.

The distinctive feature of our investigation consists in considering the AFM copper spin subsystem in a spherically symmetric approach [@spin; @spinb]. Such an approach is the most appropriate for treating the quantum 2D AFM at any finite temperature. As a result the scattering of a spin polaron by spin excitations in the singlet spin background leads to the spectral function periodicity relative to the full Brillouin zone. Note that the conventional two-sublattice spin approach leads to periodicity relative to the magnetic (reduced) Brillouin zone [@varm; @KLR; @horsch; @liu; @tj6; @plak; @kab].

The paper is organized as follows. In Section II we give the derivations for the self-consistent equation for the Green’s 