Point-form dynamics of quasistable states

TL;DR

This paper develops a field theoretical model using point-form dynamics to describe quasistable states and resonances, constructing explicit Poincaré generators and irreducible representations with complex mass.

Contribution

It introduces a novel point-form Poincaré framework for resonances, linking complex mass representations to the structure of the $S$-matrix and resonance phenomena.

Findings

Constructed explicit point-form Poincaré generators from field operators.

Identified irreducible representations characterized by complex mass and spin.

Connected complex mass to the pole of the propagator, modeling resonances.

Abstract

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.