A Moyal Quantization of the Continuous Toda Field

Details A Moyal Quantization of the Continuous Toda Field A Moyal Quantization of the Continuous Toda Field

1997-03-13

arxiv.org/abs/hep-th/9703094v3

Phys.Lett. B413 (1997) 53-62

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, revised Tex file

Scientific paper

10.1016/S0370-2693(97)01096-4

Since the lightcone self dual spherical membrane, moving in flat target backgrounds, has a direct correspondence with the $SU(\infty)$ Nahm equations and the continuous Toda theory, we construct the Moyal deformations of the self dual membrane in terms of the Moyal deformations of the continuous Toda theory. This is performed by using the Weyl-Wigner-Moyal quantization technique of the 3D continuous Toda field equation, and its associated 2D continuous Toda molecule, based on Moyal deformations of rotational Killing symmetry reductions of Plebanski first heavenly equation associated with 4D Self Dual Gravity.

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