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.