Magnetic properties of weakly doped antiferromagnets from the lagrangian t-J model

From the Lagrangian formalism for the t-J model previously developed, renormalized magnetic properties in weakly doped antiferromagnets can be evaluated. The renormalization effects essentially appear because of the interaction of particle-hole with the spin wave. For small concentration of holes the self-energies are computed. Taking an approximate form for the particle spectral function, the cuasiparticle peak and the incoherent continuum region are analyzed in order to evaluate the softening and the damping in the spin excitations of antiferromagnets weakly doped. The results can be confronted with previous one obtained by means of the Hamiltonian t-J model in the slave-fermion Schwinger boson representation.