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of such a choice of n Poisson-commuting functions. The metaplectic correction (also known as the half-form correction) is a technical modification of the above procedure that is necessary in the case of real polarizations and often convenient for complex polarizations.

Prequantization

Suppose is a symplectic manifold with symplectic form . Suppose at first that is exact, meaning that there is a globally defined symplectic potential with . We can consider the "prequantum Hilbert space" of square-integrable functions on (with

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