Acta Physica Polonica B

Vol. 29, No. 3, March 1998, page 549

Geometry Associated with Self-Dual Yang--Mills and the Chiral Model Approaches to Self-Dual Gravity

H. Garcia-Compean, J.F. Plebanski, M. Przanowski

A geometric formulation of the Moyal deformation for the self-dual Yang--Mills theory and the Chiral Model approach to self-dual gravity is given. We find in Fedosov's geometrical construction of deformation quantization the natural geometrical framework associated to the Moyal deformation of the six-dimensional version of the second heavenly equation and the Park--Husain heavenly equation. The Wess--Zumino--Witten-like Lagrangian of self-dual gravity is reexamined within this context.

PACS numbers: 04.40.--b, 11.15.--q, 11.30.Rd


 
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