Semigroup integrability of point-form dynamics

We study the integrability of Poincaré algebras for a collection of interacting particles. Using point-form dynamics, we will explicitly construct a pair of rigged Hilbert spaces in which a subset of the Poincaré algebra integrates to a differentiable representation of the causal Poincaré semigroup, the semidirect product of the Lorentz group and the semigroup of spacetime translations into the forward light cone. We will also give an example of a rigged Hilbert space in which the point-form algebra integrates to a differentiable representation of the Poincaré group. The representations of the Poincaré semigroup provide a means of understanding relativistic resonances and decaying states by way of a unified state vector description and thereby uniquely and unambiguously defining their mass, width and lifetime.