Hyperbolicity of constrained Hamiltonian systems

par Prof. David HILDITCH (University of Jena)

jeudi 10 oct. 2013, 16:45 → 17:45 Europe/Paris

Amphithéâtre Léon Motchane (Institut des Hautes Etudes Scientifiques)

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.