On Diff(S^1) Covariantization Of Pseudodifferential Operator

Details On Diff(S^1) Covariantization Of Pseudodifferential Operator On Diff(S^1) Covariantization Of Pseudodifferential Operator

1993-09-13

arxiv.org/abs/hep-th/9309070v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages

Scientific paper

10.1063/1.530626

A study of diff($S^1$) covariant properties of pseudodifferential operator of integer degree is presented. First, it is shown that the action of diff($S^1$) defines a hamiltonian flow defined by the second Gelfand-Dickey bracket if and only if the pseudodifferential operator transforms covariantly. Secondly, the covariant form of a pseudodifferential operator of degree n not equal to 0, 1, -1 is constructed by exploiting the inverse of covariant derivative. This, in particular, implies the existence of primary basis for W_{KP}^{(n)} (n not equal to 0, 1, -1).

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