Space−time symmetries and nonunitary representations of the Poincaré semigroup: Description of unstable particles

In this paper we justify the use of nonunitary representations of the space−time symmetry group to describe physical systems, as, e.g., unstable particles. It is shown that such a generalization of the standard theory of symmetries is possible inside the approach to quantum mechanics recently developed by Ludwig. The Poincaré semigroup turns out to be the fundamental symmetry group and only Lorentz transformations must be unitary.