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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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