From the text: Exact solutions of Heisenberg equations and two-particle eigenvalue problems for the nonrelativistic four-fermion interaction and an \(N,\Theta\) model are obtained in the framework of a dynamical mapping method. Equivalence of different dynamical mappings is shown.
The authors demonstrate the convenience to use Schrödinger fields (SF) \(\Psi_\alpha (\vec x,0)\) as physical ones instead of the asymptotical fields (AF) \(\psi_{in} (x)\) on exactly solvable four-fermion and \(N,\Theta\) models. The point is that SF and HF \(\Psi_\alpha (\vec x,t)\), contrary to AF, form a complete irreducible representation of CCR (CAR) also in the presence of bound states, whereas a complete set of AF must incorporate a new field for every bound state. Thus, the dynamical mapping of HF onto SF is simpler than on AF and, for several cases, may be found in closed form.