Generators of Coordinate Transformations in the Penrose Formalism of General Relativity

Publisher Website
Google Scholar
Abstract
A new covariant expression for the generator of coordinate transformations is developed in the general theory of relativity. It is hoped that this expression may facilitate the determination of the commutation relations between the independent dynamical variables of Penrose. Since the Penrose function is defined on a characteristic surface, a program for quantization is discussed which can be applied to dynamical variables defined on such null surfaces. In addition, the relationship of the new conservation law to the usual physical constants of Lorentz-covariant theories is indicated, the relationship being effected when there exists a Killing bivector in the Riemannian manifold.