Generalized Heisenberg algebra from $o(2,4)$

Abstract

It is well known that the algebra $o(2,4)$ generates the conformal group, but it can also be used to define some variants of the Yang model of noncommutative geometry on a curved spacetime. Starting from these examples, we construct a new physical model based on $o(2,4)$, that can be interpreted as a generalization of the Heisenberg algebra on phase space, with flat positions and momenta, but nontrivial commutation relations between positions and momenta and with the Planck constant promoted to an operator.