Theoretical Framework for Relativistic Resonances

To obtain a consistent mathematical theory that unifies resonance scattering and decay phenomena one has to modify the axiom of quantum mechanics that specifies the boundary conditions of the dynamical equations and choose Hardy spaces of the lower complex energy plane for the Schrodinger equation (of states) and of the upper complex energy plane for the Heisenberg equation (of observables). This theory can be extended into the relativistic domain where it provides a unique definition of the lineshape and the mass and width for relativistic resonances.