2000/08/31 by I. Benkaddour, M. Hssaini, M. Kessabi +2
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
published as International Journal of Theoretical Physics, Vol. 41, No.12, December 2002 · 31 pages
arxiv created 2003/08/07 · arxiv updated 2009/11/30
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.