Eigenvalues of the Weyl operator as observables of general relativity

Abstract

We consider the eigenvalues of the three-dimensional Weyl operator defined in terms of the (Euclidean) Ashtekar variables, and we study their dependence on the gravitational field. We notice that these eigenvalues can be used as gravitational variables, and derive explicit formulas for their Poisson brackets and their time evolution.Comment: 15 pages, LaTex style, preprint UPRF-94-39