  We mainly study real Klein-Gordon theory on Anti de Sitter spacetimes, and
apply the General Boundary Formulation (GBF) of Quantum Theory in order to
compute a radial S-matrix. We consider first the classical theory, giving a
complete list of Klein-Gordon solutions and the actions of the isometries of
AdS on them. We study two symplectic structures on spaces of such solutions,
and show that they are invariant under all isometries' actions. We also
calculate the flat limits of the involved quantities, and find that it
reproduces the respective counterparts of the theory on Minkowski spacetime. We
proceed applying Holomorphic Quantization, whose amplitudes are determined by
an inner product which is induced by the symplectic structure together with a
complex structure on the space of classical solutions. We construct this
complex structure such that the inner product becomes positive-definite, and
its induced amplitudes are invariant under time-translations and spatial
rotations. Further, our complex structure makes these radial amplitudes agree
with the amplitudes of states on equal-time hypersurfaces, and also reproduce
the amplitudes of the theory on Minkowski spacetime in the flat limit. (There
is also a more detailed summary at the beginning of the document.)
