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arXiv · hep-th/9305169

Nonabelian KP hierarchy with Moyal algebraic coefficients

Kanehisa Takasaki
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Abstract

A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new hierarchy can be interpreted as large-$N$ limit of multi-component ($\gl(N)$ symmetric) KP hierarchies. Actually, two different hierarchies are constructed. The first hierarchy consists of commuting flows and may be thought of as a straightforward extension of the ordinary and multi-component KP hierarchies. The second one is a hierarchy of noncommuting flows, and related to Moyal algebraic deformations of selfdual gravity. Both hierarchies turn out to possess quasi-classical limit, replacing Moyal algebraic structures by Poisson algebraic structures. The language of W-infinity algebras provides a unified point of view to these results.

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Kanehisa Takasaki. 1993-05-29. Nonabelian KP hierarchy with Moyal algebraic coefficients. https://doi.org/10.1016/0393-0440(94)90040-x

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