Giovanni Landi Eigenvalues as Dynamical Variables (47K, latex) ABSTRACT. We 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.