Elementary example of exact effective-Hamiltonian computation

We present an exact computation of effective Hamiltonians for elementary model obtained from the Yukawa theory by going to limit bare fermions being infinitely heavy and bosons at rest with respect that emit or absorb them. The coupling constant can be arbitrarily large. are computed solving differential equation renormalization group procedure particles (RGPEP). Physical fermions, defined in as eigenstates Hamiltonians, form fermion dressed a coherent state bosons. illustrates method used perturbative computations realistic theories. It shows mechanism which expansion Tamm-Dancoff approximation increase accuracy along RGPEP evolution.