Mariusz Hynek: Reducibile vs irreducible quantization

In the seminar two weeks ago we learned about the mathematical origins of Quantum Mechanics for the purpose of Loop Quantum Cosmology (Stone-von Neumann (SvN) theorem, Canonical Commutation Relations(CCR) etc). Here I want to discuss the procedure of quantization in more details, especially in cases when one leaves out the assumption of irreducibility of the CCR's. Then the SvN theorem does not work anymore and one gets a whole bunch of new ("enhanced by reducibility") quantum theories governed by (in general) non-Schrödinger, but solvable operators arising from classical systems with confining potentials.