Differentiable Representations of Causal Poincare Semigroup: Applications to Resonance Scattering and Decay
Causal Poincare Semigroup is the semidirect product of the Lorentz group and the semigroup of spacetime translations into the forward light cone. We will present a class of representations of this semigroup, constructed in a rigged Hilbert space under point form dynamics. These representations provide a natural framework for understanding resonances and decaying states in the relativistic realm. Within this framework, unique and unambiguous definitions of resonance mass and width can be obtained.