Dynamical inverse problem of representation theory and noncommutative geometry

TL;DR

This paper explores the dynamical inverse problem in representation theory and noncommutative geometry, illustrating foundational concepts through simple examples rooted in quantum mechanics and the determination of commutation relations.

Contribution

It introduces the dynamical inverse problem within the context of representation theory and noncommutative geometry, connecting it to classical quantum mechanics.

Findings

Illustrated the inverse problem with simple examples

Connected the problem to quantum dynamical equations

Highlighted the role of commutation relations in quantum mechanics

Abstract

Dynamical inverse problem of representation theory, which has its origin in a classical paper of E.P.Wigner on a determination of commutation relations of quantum mechanical quantities by the quantum dynamical equations, is illustrated on the simplest examples.