Kinematic Correlations of Decay Products and the State Spaces of the Relativistic Gamow Vector

This article summarizes a talk given at the XXVth International Congress on Group Theoretical Methods in Physics. The linear topological spaces of states and observables appropriate for discussing scattering are discussed. The properties of such spaces are crucial to understanding the relativistic Gamow vector, a vector description for relativistic unstable particles, and are useful for discussing kinematics correlations of decay products.