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Élie Cartan's invariant integral formalism is extended to gauge field theory, including general relativity. This constitutes an alternative procedure, as shown in several examples, that is equivalent when no second class constraints are present to the Rosenfeld, Bergmann, Dirac algorithm. In addition, a Hamilton–Jacobi formalism is developed for constructing explicit phase space functions in general relativity that are invariant under the full four-dimensional diffeomorphism group. These identify equivalence classes of classical solutions of Einstein's equations. Each member is dependent on intrinsic spatial coordinates and also undergoes non-trivial evolution in intrinsic time. Furthermore, the construction yields series expansion solutions of the field equations for all of the components of the metric tensor, including lapse and shift, in the intrinsic temporal and spatial coordinates. The intrinsic coordinates are determined by the spacetime geometry in terms of Weyl scalars. The implications of this analysis for an eventual quantum theory of gravity are profound. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This interview is focused on university studies and early career in relativity physics including thesis work under Leopold Infeld dealing with gravitational waves. Trautman's recollections include the collaboration with Ivor Robinson and relationships with relevant personalities like Felix Pirani, Jerzy Plebanski, Roger Penrose and Peter Bergmann. [ABSTRACT FROM AUTHOR]

This commentary reflects on the 1930 general theory of Léon Rosenfeld dealing with phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article in the context of ideas pursued by W. Pauli, F. Klein, E. Noether. We then comment on Rosenfeld's General Theory dealing with symmetries and constraints, symmetry generators, conservation laws and the construction of a Hamiltonian in the case of phase-space constraints. It is remarkable that he was able to derive expressions for all phase space symmetry generators without making explicit reference to the generator of time evolution. In his Applications, Rosenfeld treated the general relativistic example of Einstein-Maxwell-Dirac theory. We show, that although Rosenfeld refrained from fully applying his general findings to this example, he could have obtained the Hamiltonian. Many of Rosenfeld's discoveries were re-developed or re-discovered by others two decades later, yet as we show there remain additional firsts that are still not recognized in the community. [ABSTRACT FROM AUTHOR]

We consider the semiclassical quantization of the Klein-Gordon field on a Robertson-Walker background with a flat-out region. We show that the requirement that the energy density of created particles be finite selects a preferred equivalence class of particle definitions. We present a representative element of the equivalence class so determined. We briefly discuss the generalization to Bianchi I spacetimes, and the case of an external Maxwell field. [ABSTRACT FROM AUTHOR]