Evolution of quantum observables: from non-commutativity to commutativity

A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. One way to describe this transition is to consider the Gamow vectors, which introduce exponential decays in the evolution. In this paper, we give two mathematical models in which this transition happens in the infinite time limit. In the first one, we consider operators acting on the space of the Gamow vectors, which represent quantum resonances. In the second one, we use an algebraic formalism from scattering theory. We construct a non-commuting algebra which commutes in the infinite time limit.Fil: Fortin, Sebastian Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; ArgentinaFil: Gadella, M.. Universidad de Valladolid; EspañaFil: Holik, Federico Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Losada, Marcelo Adrián. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentin