  We introduce a dynamical evolution operator for dealing with unstable
physical process, such as scattering resonances, photon emission, decoherence
and particle decay. With that aim, we use the formalism of rigged Hilbert space
and represent the time evolution of quantum observables in the Heisenberg
picture, in such a way that time evolution is non-unitary. This allows to
describe observables that are initially non-commutative, but become commutative
after time evolution. In other words, a non-abelian algebra of relevant
observables becomes abelian when times goes to infinity. We finally present
some relevant examples.
