Hamiltonian description of the parametrized scalar field in bounded spatial regions Articles uri icon

publication date

  • April 2016

start page

  • 105002

issue

  • 10

volume

  • 33

International Standard Serial Number (ISSN)

  • 0264-9381

Electronic International Standard Serial Number (EISSN)

  • 1361-6382

abstract

  • 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.

keywords

  • parametrized field theories; bounded domains; hamiltonian formulation