  This paper discusses several functional analytic issues relevant for field
theories in the context of the Hamiltonian formulation for a free, massless,
scalar field defined on a closed interval of the real line. The fields that we
use belong to a Sobolev space with a scalar product. As we show this choice is
useful because it leads to an explicit representation of the points in the
fibers of the phase space (the cotangent bundle of the configuration space).
The dynamical role of the boundary of the spatial manifold where the fields are
defined is analyzed.
