The notion of deformation quantization, which is a deformation of Poisson algebras, has been formulated beautifully by Bayen et al [B] to describe quantum mechanics from the algebraic point of view. The fundamental idea of deforming Poisson algebras is roughly to quantize commutative algebras in the spirit of microlocal analysis (cf. [BG]). According to the remarkable description by Guillemin Steinberg [GS], a crucial point in microlocal analysis is a selection of the asymptotics usually expressed in terms of a parameter.
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