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A One-Parameter Family of Hamiltonian Structures for the KP Hierarchy and a Continuous Deformation of the Nonlinear $W_{
m KP}$ Algebra | | J.M. Figueroa-O’Farrill
; J. Mas
; E. Ramos
; | | Date: |
28 Jul 1992 | | Journal: | Commun.Math.Phys. 158 (1993) 17-44 | | Subject: | hep-th | | Abstract: | The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting $W$-algebra is a one-parameter deformation of $W_{
m KP}$ admitting a central extension for generic values of the parameter, reducing naturally to $W_n$ for special values of the parameter, and contracting to the centrally extended $W_{1+infty}$, $W_infty$ and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic to $w_{
m KP}$. The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of $widehat{W}_infty$ which contracts to a new nonlinear algebra of the $W_infty$-type. | | Source: | arXiv, hep-th/9207092 | | Services: | Forum | Review | PDF | Favorites | |
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