The metaplectic correction in Kähler quantization is a result of the introduction of the half-form structure when considering geometric quantization over Kähler manifolds. This correction is a very interesting topic, since no mathematical argument can prove or reject its necessity, and only a physical consideration can point to an answer. As a result, no universally accepted reason for considering such a structure has been identified in the context of quantization theory. In this letter, we view this topic not in a quantization context, but as a means to understand an exact connection between the canonical and path integral formulation of quantum mechanics. More specifically, we investigate whether or not the contribution of the metaplectic correction is related to the recent results found in the context of coherent-state path integrals, regarding the “correct” identification of the continuum limit. We then use the theory of coherent-state path integrals as a template, and our results indeed point to the necessity of this correction.

考虑到Kähler流形上的几何量化时，引入半形式结构的结果是Kähler量化中的元偏校正。这种校正是一个非常有趣的话题，因为没有任何数学论据可以证明或拒绝其必要性，只有物理上的考虑才能指出答案。结果，在量化理论的背景下，尚未发现考虑这种结构的普遍接受的理由。在这封信中，我们认为本主题不是在量化的背景下进行，而是作为一种理解量子力学的规范和路径积分公式之间确切联系的方式。更具体地说，我们研究了元偏角校正的作用是否与在相干态路径积分的情况下发现的最新结果有关，关于连续极限的“正确”标识。然后，我们使用相干态路径积分理论作为模板，我们的结果确实指出了进行此校正的必要性。