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We show that the real massive Klein-Gordon theory admits a description interms of states on various timelike hypersurfaces and amplitudes associated toregions bounded by them. This realizes crucial elements of the general boundaryframework for quantum field theory. The hypersurfaces considered arehyperplanes on the one hand and timelike hypercylinders on the other hand. Thelatter lead to the first explicit examples of amplitudes associated with finiteregions of space, and admit no standard description in terms of ``initial'' and``final'' states. We demonstrate a generalized probability interpretation inthis example, going beyond the applicability of standard quantum mechanics.Comment: 25 pages, LaTeX; typos correcte

General boundary quantum field theory: Timelike hypersurfaces in the Klein-Gordon theory