Hamiltonian description of the parametrized scalar field in bounded spatial regions

Understand

We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions.

• We generalize the work carried out by a number of authors on parametrized field systems to the interesting case where spatial boundaries are present.
• The configuration space of our models contains both smooth scalar fields defined on the spatial manifold and spacelike embeddings from the spatial manifold to a target spacetime endowed with a fixed Lorentzian background metric.
• We pay particular attention to the geometry of the infinite dimensional manifold of embeddings and the description of the relevant geometric objects: the symplectic form on the primary constraint submanifold and the Hamiltonian vector fields defined on it.