Algebraic quantization

The different correspondences (or orderings) used in quantum mechanics and the associated deformations, are both seen from an algebraic viewpoint. The deformations which are compatible with the diagonal map (the ₀-deformations) are introduced and connected to the formal groups. A very straighforward example of a ₀-deformation (the multiplicative deformation) appears in the normal quantization of the harmonic oscillator.