On the quantum KP hierarchy and its relation to the non-linear Schrödinger equation

Details On the quantum KP hierarchy and its relation to the non-linear Schrödinger equation On the quantum KP hierarchy and its relation to the non-linear Schrödinger equation

1992-08-04

arxiv.org/abs/hep-th/9208013v1

Phys.Lett. B295 (1992) 59-66

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, KCL-TH-92-2

Scientific paper

10.1016/0370-2693(92)90089-M

We establish a relation between the classical non-linear Schr\"odinger equation and the KP hierarchy, and we extend this relation to the quantum case by defining a quantum KP hierarchy. We present evidence that an integrable hierarchy of equations is obtained by quantizing the first Hamiltonian structure of the KdV equation. The connection between infinite-dimensional algebras and integrable models is discussed.

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