The space of physical states in relativistic scattering theory is
constructed, using a rigorous version of the Dirac formalism, where the Hilbert
space structure is extended to a Gel'fand triple. This extension enables the
construction of ``a complete set of states'', the basic concept of the original
Dirac formalism, also in the cases of unbounded operators and continuous
spectra. We construct explicitly the Gel'fand triple and a complete set of
``plane waves'' -- momentum eigenstates -- using the group of space-time
symmetries. This construction is used (in a separate article) to prove a
generalization of the Coleman-Mandula theorem to higher dimension.Comment: 30 pages, Late