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Quantum nonlinear Schrödinger equation. I: Intertwining operators. (English) Zbl 0614.35086
The quantum nonlinear Schrödinger equation is studied as a model of the quantum (nonrelativistic) field theory in \(1+1\) dimensions. In § 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 § 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.
Reviewer: J.Weidmann

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35G20 Nonlinear higher-order PDEs
81T08 Constructive quantum field theory
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