ANTILOCALITY AND A REEH-SCHLIEDER THEOREM ON MANIFOLDS

It is shown that the operator A1/2, where A is any positive self-adjoi nt extension of a positive operator of the form '- Laplace-Beltrami op erator + potential' on an n-dimensional Riemannian manifold, is strong ly antilocal. Using this result, a Reeh-Schlieder theorem for the cano nical vacuum of the Klein-Gordon field propagating in ultrastatic spac etimes is derived. In a further application, we gain weaker versions o f the Reeh-Schlieder theorem for more general situations.