6 papers
Deformation Quantization of sdiff() SDYM Equation
M. Przanowski, J. F. Plebanski, S. Formanski
Deformation quantization (the Moyal deformation) of SDYM equation for the algebra of the area preserving diffeomorphisms of a 2-surface , sdiff(), is studied. Deforme…
Matrix representation of the generalized Moyal algebra
Jerzy F. Plebanski, Maciej Przanowski, Francisco J. Turrubiates
It is shown that the isomorphism between the generalized Moyal algebra and the matrix algebra follows in a natural manner from the generalized Weyl quantization rule and from the w…
Non-vacuum twisting type N metrics
Paweł~Nurowski, Jerzy F. Plebański
A maximally reduced system of equations corresponding to the twisting type N Einstein metrics is given. When the cosmological constant they reduce to the standard equation…
A note on the iterative approach to twisting type N solutions
L. Palacios, J. F. Plebanski
We present the results of the computation of a twisting type N solution to vacuum Einstein equations following an iterative approach. Our results show that the higher order terms f…
The Geometry of Deformation Quantization and Self-Dual Gravity
Hugo Garcia-Compean, Jerzy F. Plebanski, Maciej 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 c…
Differential Forms, Hopf Algebra and General Relativity I
Jerzy F. Plebanski, G. R. Moreno, F. J. Turrubiates
We review the language of differential forms and their applications to Riemannian Geometry with an orientation to General Relativity. Working with the principal algebraic and diffe…