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

M. Przanowski; J. F. Plebanski; S. Formanski

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arXiv · hep-th/0107211

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

M. Przanowski·J. F. Plebanski·S. Formanski

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Abstract

Deformation quantization (the Moyal deformation) of SDYM equation for the algebra of the area preserving diffeomorphisms of a 2-surface $Σ_{2}$, sdiff($Σ_{2}$), 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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M. Przanowski, J. F. Plebanski, S. Formanski. 2001-07-24. Deformation Quantization of sdiff($Σ_{2}$) SDYM Equation. https://arxiv.org/abs/hep-th/0107211

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