ANTILOCALITY AND A REEH-SCHLIEDER THEOREM ON MANIFOLDS

It is shown that the operator A1/2, where A is any positive self-adjoint extension of a positive operator of the form '- Laplace-Beltrami operator + potential' on an n-dimensional Riemannian manifold, is strongly antilocal. Using this result, a Reeh-Schlieder theorem for the canonical vacuum of the Klein-Gordon field propagating in ultrastatic spacetimes is derived. In a further application, we gain weaker versions of the Reeh-Schlieder theorem for more general situations.