Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-04-23
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 29 pages. To be published in J.Geom.Phys
Scientific paper
10.1016/S0393-0440(96)00019-8
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one obtains a geometric description of the operators. A dual theory is also possible, based on a deformation of differential forms. This calculus is applied to a number of multidimensional integrable systems, such as the KP hierarchy, thus obtaining a geometrical description of these systems. The limit in which the deformation disappears corresponds to taking the dispersionless limit in these hierarchies.
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