Algebra of Deformed Differential Operators and Induced Integrable Toda Field Theory

Details Algebra of Deformed Differential Operators and Induced Integrable Toda Field Theory Algebra of Deformed Differential Operators and Induced Integrable Toda Field Theory

2000-08-14

arxiv.org/abs/hep-th/0008113v2

International Journal of Theoretical Physics, Vol. 41, No.12, December 2002

Physics

High Energy Physics

High Energy Physics - Theory

31 pages

Scientific paper

We build in this paper the algebra of q-deformed pseudo-differential operators shown to be an essential step towards setting a q-deformed integrability program. In fact, using the results of this q-deformed algebra, we derive the q-analogues of the generalized KdV hierarchy. We focus in particular on the first leading orders of this q-deformed hierarchy namely the q-KdV and q-Boussinesq integrable systems. We present also the q-generalization of the conformal transformations of the currents and discuss the primarity condition of the fields by using the Volterra gauge group transformations for the q-covariant Lax operators. An induced su(n)-Toda(su(2)-Liouville) field theory construction is discussed and other important features are presented.

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