angular momentum squared operator, but it further contains a constant term . (This extra term offset is pedagogically significant, since it accounts for the nonvanishing angular momentum of the ground-state Bohr orbit in the hydrogen atom, even though the standard QM ground state of the atom has vanishing .) As a mere representation change, however, Weyl's map is useful and important, as it underlies the alternate equivalent phase space formulation of conventional quantum mechanics. Geometric quantization In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest. For example, the similarity between the Heisenberg equation in the Heisenberg picture of quantum mechanics and the Hamilton equation in classical physics should be built in. A more geometric approach to quantization, in which the classical phase space can be a general symplectic manifold, was developed in the 1970s by Bertram Kostant and Jean-Marie Souriau. The method proceeds in two stages. First, once constructs a "prequantum Hilbert space" consisting of square-integrable functions (or, more properly, sections of a line bundle) over the phase space. Here one can construct operators satisfying commutation relations corresponding exactly to the classical Poisson-bracket relations. On the other hand, this prequantum Hilbert space is too big to be physically meaningful. One then restricts to functions (or sections) depending on half the variables on the phase space, yielding the quantum Hilbert space. Loop quantization See Loop quantum gravity. Path integral quantization A classical mechanical theory is given by an action with the permissible configurations being the ones which are extremal with respect to functional variations of the action. A quantum-mechanical description of the classical system can also be constructed from the action of the system by means of the path integral formulation. Quantum statistical mechanics approach See Uncertainty principle. Schwinger's variational approach See Schwinger's quantum action principle. See also First quantization Feynman path integral Light front quantization Photon polarization Quantum Hall effect Quantum number Stochastic quantization References Abraham, R. & Marsden (1985): Foundations of Mechanics, ed. Addison–Wesley, Ali, S. T., & Engliš, M. (2005). "Quantization methods: a guide for physicists and analysts". Reviews in Mathematical Physics 17 (04), 391-490. G. Giachetta, L. Mangiarotti, G. Sardanashvily, Geometric and Algebraic Topological