Séminaires sur les aspects théoriques et expérimentaux de la gravitation

Hyperbolicity of constrained Hamiltonian systems

by Prof. David HILDITCH (University of Jena)

Europe/Paris
Amphithéâtre Léon Motchane (Institut des Hautes Etudes Scientifiques)

Amphithéâtre Léon Motchane

Institut des Hautes Etudes Scientifiques

Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description
Motivated by the question, "what coordinates choices are `good' for general relativity?" I will discuss gauge theories from the from the free evolution point of view, in which initial data satisfying constraints of a theory are given, and because the constraints are compatible with the field equations they remain so. I will present a model constrained Hamiltonian theory and identify a particular structure in the equations of motion from which statements can be made about the status of the initial value problem, just by examining a subset of the equations, called the pure gauge subsystem. I will then present the application of these ideas to GR, which results in a five parameter generalization of the `good' gauge used in Choquet-Bruhat's original treatment of the initial value problem.
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