Eigenvalues as Dynamical Variables

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.

14 pages, Latex. Based on a talk given at the Arbeitstagung `Das Standardmodell der Elementarteilchenphysik unter mathematisch-geometrischem Aspekt', Hesselberg, Germany, March 1999