The remarkable quantum phenomenon of 'non-locality' discovered by Einstein, Podolsky and Rosen (EPR) is the centre of considerable experimental and theoretical activity these days. Nevertheless, many (perhaps most) physicists do not feel the phenomenon is especially paradoxical, or even worthy of interest. This article attempts to reveal, in a simple way, just where the fascination of the EPR paradox lies, and to answer some of the arguments invoked by critics to 'explain away' the paradox.
The conditions that must be fulfilled by a certain physical system to apply geometric quantization prescription on it are investigated. These terms are sought as mathematical requirements, which can be traced in an analysis of integrable systems, from the perspective of both potential function and Hamiltonian vector field. The answer is found in momentum map critical points. Basically, a certain disposal of points that allow a momentum map
C∗ isomorphism, of observables, with harmonic oscillator momentum map enforce geometric quantization rules. Following the general theory, two newly presented examples, which exhibits these properties, are quantified through geometric quantization prescription. The Lennard-Jones' type potential is one of the examples, it is known as describing molecules in interaction. We end with a third example that shows the local isomorphism of potentials do not induce
C∗ isomorphism of observables.