Geometric quantization is applied to infinite (countable) dimensional linear Kähler manifolds to obtain a closed expression for the anomalous commutator of arbitrary polynomial observables. Examples for the physical relevance of the result are given, including the polarization dependence of Schwinger terms in bilinear constraint algebras, the central terms of Virasoro and Kac-Moody algebras and the determination of the critical dimension of the bosonic string.
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