Quantum nonlinear Schrödinger equation. I: Intertwining operators (Q1820332)

The quantum nonlinear Schrödinger equation is studied as a model of the quantum (nonrelativistic) field theory in \(1+1\) dimensions. In {\S} 1 the calculus of intertwining operators \(P_ N\), \(P^*_ N\), \(P_ N^{*- 1}\), \(P_ N^{-1}\) on \({\mathcal H}_ N\) is developed which produce the equivalence of the N-particle Hamiltonian \(H_ N\) and the free Hamiltonian \(-\Delta_ N\). In {\S} 2 the intertwining operators on the Fock space are studied, which are the direct sums of the corresponding operators on \({\mathcal H}_ N\). This calculus is supposed to be the basis for subsequent publications on the explicit solution of an initial value problem for the nonlinear Schrödinger equation.