  A self-consistent, spin rotational invariant Green's function procedure has
been developed to calculate the spectral function of carrier excitations in the
spin-fermion model for the CuO2 plane. We start from the mean field description
of a spin polaron in the Mori-Zwanzig projection method. In order to determine
the spin polaron lifetime in the self-consistent Born approximation, the
self-energy is expressed by an irreducible Green's function. Both, spin polaron
and bare hole spectral functions are calculated. The numerical results show a
well pronounced quasiparticle peak near the bottom of the dispersion at
(pi/2,pi/2), the absence of the quasiparticle at the Gamma-point, a rather
large damping away from the minimum and an asymmetry of the spectral function
with respect to the antiferromagnetic Brillouin zone. These findings are in
qualitative agreement with photoemission data for undoped cuprates. The direct
oxygen-oxygen hopping is responsible for a more isotropic minimum at
(pi/2,pi/2).
