A one-parameter family of hamiltonian structures for the KP hierarchy and a continuous deformation of the nonlinear WKP algebra |
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| Authors: | José M Figueroa-O'Farrill Javier Mas Eduardo Ramos |
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| Institution: | (1) Physikalisches Institut der Universität Bonn, Nußalle 12, D-53115 Bonn, Germany;(2) Departamento de Física de Partículas Elementales, Universidad de Santiago, E-15706 Santiago de Compostela, Spain;(3) Instituut voor Theoretische Fysica, Universiteit Leuven, Celestijnenlaan 200D, B-3001 Heverlee, Belgium |
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| 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 WKP 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 W1+ , W and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic tow
KP. The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of
which contracts to a new nonlinear algebra of the W-type.Address after October 1993: Queen Mary and Westfield College, UK |
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