Dynamical correspondence in algebraic Lagrangian geometry

In this paper, which is a continuation of [12], we develop the idea of applying Abelian Lagrangian algebraic geometry (see [3], [4], [10], [11]) to geometric quantization. The Dirac correspondence principle holds for this ALG(a)-quantization. The known models of geometric quantization involving the choice of real or complex polarizations are presented as reductions (or linearizations) of the proposed quantization. This enables us to link the results of known constructions that use polarizations.