The wave equation (free boson) problem is studied from the viewpoint of the
relations on the symplectic manifolds associated to the boundary induced by
solutions. Unexpectedly there is still something to say on this simple,
well-studied problem. In particular, boundaries which do not allow for a
meaningful Hamiltonian evolution are not problematic from the viewpoint of
relations. In the two-dimensional Minkowski case, these relations are shown to
be Lagrangian. This result is then extended to a wide class of metrics and is
conjectured to be true also in higher dimensions for nice enough metrics. A
counterexample where the relation is not Lagrangian is provided by the Misner
space.Comment: 27 pages; minor clarifying changes added; to appear in CM
