Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-02-05
J.Geom.Phys. 33 (2000) 173-190
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, revised Tex file. A discussion of the chiral approach to Self Dual Gravity is added to the previous Yang Mills one
Scientific paper
A geometric derivation of $W_\infty$ Gravity based on Fedosov's deformation quantization of symplectic manifolds is presented. To lowest order in Planck's constant it agrees with Hull's geometric formulation of classical nonchiral $W_\infty$ Gravity. The fundamental object is a ${\cal W}$-valued connection one form belonging to the exterior algebra of the Weyl algebra bundle associated with the symplectic manifold. The ${\cal W} $-valued analogs of the Self Dual Yang Mills equations, obtained from a zero curvature condition, naturally lead to the Moyal Plebanski equations, furnishing Moyal deformations of self dual gravitational backgrounds associated with the complexified cotangent space of a two dimensional Riemann surface. Deformation quantization of $W_\infty$ Gravity is retrieved upon the inclusion of all the $\hbar$ terms appearing in the Moyal bracket. Brief comments on Non Commutative Geometry and M(atrix)theory are made.
No associations
LandOfFree
W-Geometry from Fedosov's Deformation Quantization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with W-Geometry from Fedosov's Deformation Quantization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and W-Geometry from Fedosov's Deformation Quantization will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-253166