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We mainly study real Klein-Gordon theory on Anti de Sitter spacetimes, andapply the General Boundary Formulation (GBF) of Quantum Theory in order tocompute a radial S-matrix. We consider first the classical theory, giving acomplete list of Klein-Gordon solutions and the actions of the isometries ofAdS on them. We study two symplectic structures on spaces of such solutions,and show that they are invariant under all isometries' actions. We alsocalculate the flat limits of the involved quantities, and find that itreproduces the respective counterparts of the theory on Minkowski spacetime. Weproceed applying Holomorphic Quantization, whose amplitudes are determined byan inner product which is induced by the symplectic structure together with acomplex structure on the space of classical solutions. We construct thiscomplex structure such that the inner product becomes positive-definite, andits induced amplitudes are invariant under time-translations and spatialrotations. Further, our complex structure makes these radial amplitudes agreewith the amplitudes of states on equal-time hypersurfaces, and also reproducethe amplitudes of the theory on Minkowski spacetime in the flat limit. (Thereis also a more detailed summary at the beginning of the document.)

General Boundary Quantum Field Theory in Anti de Sitter Spacetimes