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تسجيل مستخدم جديدNo anomalous canonical commutators induced by Berrys phase
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The monopole-like singularity of Berrys 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 Berrys model, we show that Berrys phase does not lead to the deformation of the principle of quantum mechanics in the sense of anomalous canonical commutators. If one should assume Berrys 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 Berrys phase of the genuine Dirac monopole-type is not supported by the exactly solvable version of Berrys model nor by a generic model of Berrys phase. Besides, the monopole-like Berrys phase in momentum space has a magnetic charge $e_{M}=2pihbar$, for which the possible anomalous term in the canonical commutator $[x_{k},x_{l}]=ihbarOmega_{kl}$ would become of the order $O(hbar^{2})$.
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