Geometric formulation of covariant phase methods with boundary

Abstract: In physics, one standard way to study and understand a theory is through its dynamical formulation. Whenever possible, this is obtained by considering some initial conditions and evolving them through the dynamical equations of the theory. One gets then a curve over the space of initial conditions which codifies the evolution. This approach is useful in many settings, including General Relativity (ADM, numerical relativity, gravitational waves...), however, it also has some limitations. Namely, to understand some non-local concepts such as black holes and their properties (e.g. spin, energy, or entropy) one runs into some complications. Another approach is to study the space of solutions where each point represents a whole solution of the theory. For well-posed problems, this space is equivalent to the space of initial conditions (each initial condition gives rise to one and only one solution) although in general there would be some gauge degeneracy (the solution is determined up to some gauge transformation). In this talk, I will present this latter approach in what is known as the Covariant Phase Space methods. In particular, I will show how to construct a presymplectic structure over the space of solutions canonically associated with the action of the theory. The novelty of our work is that we consider the manifold with boundary, which adds several difficulties that had not been solved before.

general relativity and quantum cosmologyHEP - phenomenologyHEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

HEP seminars TU Wien (Vienna)

Series comments: ID number: 954 8284 9369