On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model: II. The Quantum Case

Details On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model: II. The Quantum Case On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model: II. The Quantum Case

1992-10-21

arxiv.org/abs/hep-th/9210118v1

J.Math.Phys. 34 (1993) 5872-5896

Physics

High Energy Physics

High Energy Physics - Theory

33p

Scientific paper

10.1063/1.530287

This paper is devoted to constructing a quantum version of the famous KP hierarchy, by deforming its second Hamiltonian structure, namely the nonlinear $\hat{W}_{\infty}$ algebra. This is achieved by quantizing the conformal noncompact $SL(2,R)_{k}/U(1)$ coset model, in which $\hat{W}_{\infty}$ appears as a hidden current algebra. For the quantum $\hat{W}_{\infty}$ algebra at level $k=1$, we have succeeded in constructing an infinite set of commuting quantum charges in explicit and closed form. Using them a completely integrable quantum KP hierarchy is constructed in the Hamiltonian form. A two boson realization of the quantum $\hat{W}_{\infty}$ currents has played a crucial role in this exploration.

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