We develop a quantization method, that we name decomposable Weyl quantization, which ensures that the constants of motion of a prescribed finite set of Hamiltonians are preserved by the quantization.Our method is based on a structural analogy between the notions of reduction of the classical phase space and diagonalization of selfadjoint operators. We obtain the spectral decomposition of the emerging quantum constants of motion directly from the quantization process.If a specific quantization is given, we expect that it preserves constants of motion exactly when it coincides with decomposable Weyl quantization on the algebra of constants of motion. We obtain a characterization of when such property holds in terms of the Wigner transforms involved. We also explain how our construction can be applied to spectral theory.Moreover, we discuss how our method opens up new perspectives in formal deformation quantization and geometric quantization.

中文翻译：

---

运动常数的规范量化

我们开发了一种量化方法，我们将其命名为可分解的 Weyl 量化，它确保通过量化保留规定的有限哈密顿量集的运动常数。我们的方法基于经典相位减少概念之间的结构类比自伴算子的空间和对角化。我们直接从量化过程中获得新出现的运动量子常数的谱分解。如果给定一个特定的量化，我们期望它恰好与运动常数代数上的可分解外尔量化一致时保留运动常数。我们根据所涉及的 Wigner 变换获得了这种性质何时成立的特征。我们还解释了我们的构造如何应用于光谱理论。此外，