SINGULAR DYNAMICS OF A FERMION COUPLED TO THE PLANAR ANTIFERROMAGNET

A model for a single fermion coupled to the planar antiferromagnetic spin background via the local spin - fermion coupling is studied. Within the perturbation theory as well as the self-consistent calculation of the quasiparticle spectra the fermion self energy shows a nonanalytical behaviour SIGMA"(omega > 0) is-proportional-to omega(alpha), alpha less-than-or-equal-to 1. The original Hamiltonian is approximated with an effective single level model with a linear coupling to soft bosons. Exact results of the latter model again indicate on the orthogonality catastrophe in this system.