2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/36548We review some work done with C. Rovelli on the use of the eigenvalues of the Dirac operator on a curved spacetime as dynamical variables, the main motivation coming from their invariance under the action of diffeomorphisms. The eigenvalues constitute an infinite set of ``observables'' for general relativity and can be taken as variables for an invariant description of the gravitational field dynamics.14 pages, Latex. Based on a talk given at the Arbeitstagung `Das Standardmodell der Elementarteilchenphysik unter mathematisch-geometrischem Aspekt', Hesselberg, Germany, March 1999General Relativity and Quantum CosmologyMathematical Physicstext