某些低能量子现象的普朗克尺度效应
Planck scale effects on some low energy quantum phenomena
摘要：
几乎所有的量子引力理论都预言了海森堡不确定原理在普朗克尺度附近的修正，即所谓的广义不确定原理（GUP）。最近的研究表明，GUP引起了对薛定谔方程和狄拉克方程的修正，这反过来又影响了所有的非相对论和相对论量子哈密顿量。本文将其应用于超导和量子霍尔效应，并计算了普朗克尺度修正。我们还表明，普朗克尺度效应可以解释一个（小）部分的异常磁矩的μ子。我们获得（弱）经验界限的GUP参数从目前的实验。
英文摘要：
Almost all theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). Recently it was shown that the GUP gives rise to corrections to the Schrodinger and Dirac equations, which in turn affect all non-relativistic and relativistic quantum Hamiltonians. In this paper, we apply it to superconductivity and the quantum Hall effect and compute Planck scale corrections. We also show that Planck scale effects may account for a (small) part of the anomalous magnetic moment of the muon. We obtain (weak) empirical bounds on the undetermined GUP parameter from present-day experiments.
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