  We present a field theoretical model of point-form dynamics which exhibits
resonance scattering. In particular, we construct point-form Poincar\'e
generators explicitly from field operators and show that in the vector spaces
for the in-states and out-states (endowed with certain analyticity and
topological properties suggested by the structure of the $S$-matrix) these
operators integrate to furnish differentiable representations of the causal
Poincar\'e semigroup, the semidirect product of the semigroup of spacetime
translations into the forward lightcone and the group of Lorentz
transformations. We also show that there exists a class of \emph{irreducible}
representations of the Poincar\'e semigroup defined by a complex mass and a
half-integer spin. The complex mass characterizing the representation naturally
appears in the construction as the square root of the pole position of the
propagator. These representations provide a description of resonances in the
same vein as Wigner's unitary irreducible representations of the Poincar\'e
group provide a description of stable particles.
