Abstract
It is shown that the operatorA 1/2, whereA is any positive self-adjoint extension of a positive operator of the form ‘-Laplace-Beltrami operator +potential’ on ann-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.
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Supported by the DFG, SFB 288 ‘Differentialgeometrie und Quantenphysik’.