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Is General Relativity An "Already Parametrized" Theory?, Charles G. Torre
Is General Relativity An "Already Parametrized" Theory?, Charles G. Torre
All Physics Faculty Publications
Beginning with the work of Dirac and of Arnowitt, Deser, and Misner in the late 1950s and early 1960s, and then after subsequent development by Kuchař, the canonical dynamical structure of general relativity has often been viewed as that of a parametrized field theory in which the many-fingered spacetime variables are hidden among the geometrodynamical field variables. This paradigm of general relativity as an "already parametrized" theory forms the basis for one of the most satisfactory resolutions of the problems of time and observables in classical and quantum gravity. However, despite decades of effort, no identification of many-fingered spacetime variables …
Covariant Phase Space Formulation Of Parametrized Field Theories, Charles G. Torre
Covariant Phase Space Formulation Of Parametrized Field Theories, Charles G. Torre
All Physics Faculty Publications
Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical (pre)symplectic structure. Motivated by issues arising in general relativity, we focus on phase space representations of the space‐time diffeomorphism group, construction of observables, and the relationship between the canonical and covariant phase spaces.