A history of observables and Hamilton–Jacobi approaches to general relativity

Abstract

The main focus is on the Hamilton–Jacobi techniques in classical general relativity that were pursued by Peter Bergmann and Arthur Komar in the 1960s and 1970s. They placed special emphasis on the ability to construct the factor group of canonical transformations, where the four-dimensional diffeomorphism phase space transformations were factored out. Equivalence classes were identified by a set of phase space functions that were invariant under the action of the four-dimensional diffeomorphism group. This is contrasted and compared with approaches of Paul Weiss, Julian Schwinger, Richard Arnowitt, Stanley Deser, Charles Misner, Karel Kuchař—and especially the geometrodynamical program of John Wheeler and Bryce DeWitt where diffeomorphism symmetry is replaced by a notion of multifingered time. The origins of all of these approaches are traced to Elie Cartan’s invariant integral formulation of classical dynamics. A related correspondence concerning the thin sandwich dispute is also documented.