Deformation Quantization of sdiff($Σ_{2}$) SDYM Equation

Details Deformation Quantization of sdiff($Σ_{2}$) SDYM Equation Deformation Quantization of sdiff($Σ_{2}$) SDYM Equation

2001-07-24

arxiv.org/abs/hep-th/0107211v1

Physics

High Energy Physics

High Energy Physics - Theory

12+1 pages, latex, no figures

Scientific paper

Deformation quantization (the Moyal deformation) of SDYM equation for the algebra of the area preserving diffeomorphisms of a 2-surface $\Sigma_{2}$, sdiff($\Sigma_{2}$), is studied. Deformed equation we call the master equation (ME) as it can be reduced to many integrable nonlinear equations in mathematical physics. Two sets of concerved charges for ME are found. Then the linear systems for ME (the Lax pairs) associated with the conserved charges are given. We obtain the dressing operators and the infinite algebra of hidden symmetries of ME. Twistor construction is also done.

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