Commutation relations and finite dimensional approximations
Ponente: Fernando Lledó (ICMAT-UC3M)Fecha: martes 22 de marzo de 2022 - 13:00Lugar: Room 2.2.D08, Universidad Carlos III de Madrid
One of the most fundamental relations in quantum mechanics is the commutation relation between position and momentum, which, when written in the most simple case, is \(QP − PQ = i1\). Heisenberg attributed this "ingenious" relation to Born in a famous letter to Pauli in 1925. It soon became clear that neither matrices nor bounded operators on a Hilbert space can represent the relation. In this talk we will show that a recent \(C^*\)-algebra introduced by Buchholz and Grundling which encodes the commutation relations in terms of resolvents does allow an approximation in terms of matrices and where the commutation relations appear only asymptotically.
Reference: F. Lledó and D. Martínez, A note on commutation relations and finite dimensional approximations, preprint 2021, arXiv: math.OA:2111.15221