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Self-energy corrections due to fermion-magnon interaction are studied in theantiferromagnetic state of the $t-t'-t''$ Hubbard model within the rainbow(noncrossing) approximation in the full $U$ range from weak to strong coupling.The role of classical (mean-field) features of fermion and magnon dispersion,associated with finite $U,t',t''$, are examined on quantum corrections toquasiparticle energy, weight, one-particle density of states etc. A finite-$U$induced classical dispersion term, absent in the $t-J$ model, is found to playan important role in suppressing the quasiparticle weight for states near ${\bfk}=(0,0)$, as seen in cuprates. For intermediate $U$, the renormalized AF bandgap is found to be nearly half of the classical value, and the weak couplinglimit is quite non-trivial due to strongly suppressed magnon amplitude. Forfinite $t'$, the renormalized AF band gap is shown to vanish at a criticalinteraction strength $U_c$, yielding a spin fluctuation driven first-order AFinsulator - PM metal transition. Quasiparticle dispersion evaluated with thesame set of Hubbard model cuprate parameters, as obtained from a recent magnonspectrum fit, provides excellent agreement with ARPES data for $\rm Sr_2 Cu O_2Cl_2 $.Comment: 11 pages, 17 figure

Self-energy corrections in an antiferromagnet: Interplay of classical and quantum effects on quasiparticle dispersion