One of the major advances of science in the 20th century was the discovery of a mathematical formulation of quantum mechanics by Heisenberg in 1925 [94].1 From a mathematical point of view, this transition from classical mechanics to quantum mechanics amounts to, among other things, passing from the commutative algebra of classical observables to the noncommutative algebra of quantum mechanical observables. To understand this better we recall that in classical mechanics an observable of a system (. energy, position, momentum, etc.) is a function on a manifold called the phase space of the system. Classical observables can therefore be multiplied in a pointwise manner and this multiplication is.
