  We analyze the two-dimensional spin-fermion model in the strong coupling
regime relevant to underdoped cuprates. We recall the set of general sumrules
that relate moments of spectral density and the imaginary part of fermion
self-energy with static correlation functions. We show that two-pole
approximation of projection method satisfies the sumrules for first four
moments of spectral density and gives an exact upper bound for quasiparticle
energy near the band bottom. We prove that non-crossing approximation that is
often made in perturbative consideration of the model violates the sumrule for
third moment of spectral density. This leads to wrong position of lowest
quasiparticle band. On the other hand, the projection method is inadequate in
weak coupling limit because of approximate treatment of kinetic energy term. We
propose a generalization of projection method that overcomes this default and
give the fermion self-energy that correctly behaves both in weak and strong
coupling limits.
