Abstract The monopole-like singularity of Berry’s adiabatic phase in momentum space and associated anomalous Poisson brackets have been recently discussed in various fields. With the help of the results of an exactly solvable version of Berry’s model, we show that Berry’s phase does not lead to the deformation of the principle of quantum mechanics in the sense of anomalous canonical commutators. If one should assume Berry’s phase of genuine Dirac monopole-type, which is assumed to hold not only in the adiabatic limit but also in the non-adiabatic limit, the deformation of the principle of quantum mechanics could take place. But Berry’s phase of the genuine Dirac monopole-type is not supported by the exactly solvable version of Berry’s model nor by a generic model of Berry’s phase. Besides, the monopole-like Berry’s phase in momentum space has a magnetic charge e M = 2 π ħ , for which the possible anomalous term in the canonical commutator [ x k , x l ] = i ħ Ω k l would become of the order O ( ħ 2 ) .

中文翻译：

---

没有由 Berry 相位引起的异常规范换向器

摘要 最近，各种领域都讨论了动量空间中贝里绝热相的类单极奇点和相关的异常泊松括号。借助 Berry 模型的完全可解版本的结果，我们表明 Berry 的相位不会导致在反常正则换向器的意义上量子力学原理的变形。如果假设贝里相位是真正的狄拉克单极子型，假设它不仅在绝热极限中而且在非绝热极限中成立，量子力学原理的变形可能发生。但是真正的狄拉克单极子型的 Berry 相位不受 Berry 模型的完全可解版本和 Berry 相位的通用模型的支持。除了，