Eigenvalues of the Weyl operator as observables of general relativity

TL;DR

This paper investigates the eigenvalues of the Weyl operator in the context of general relativity, showing they can serve as gravitational variables with explicit formulas for their dynamics.

Contribution

It introduces eigenvalues of the Weyl operator as new gravitational variables and derives their Poisson brackets and evolution equations.

Findings

Eigenvalues depend on the gravitational field.

Explicit formulas for Poisson brackets.

Time evolution equations derived.

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.