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Possibility of small electron states
Physical Review A ( IF 2.9 ) Pub Date : 2020-11-30 , DOI: 10.1103/physreva.102.052225
Charles T. Sebens

Some authors have claimed that there exists a minimum size (on the order of the Compton radius) for electron states composed entirely of positive-frequency solutions to the free Dirac equation. Other authors have put forward counterexamples to such claims. This article asks how the counterexamples of A. J. Bracken and G. F. Melloy [J. Phys. A. 32, 6127 (1999)] bypass two arguments against their possibility. The first is an old argument that, because of the prohibition on faster-than-light motion, the electron must be larger than a certain minimum size if it is to have the correct angular momentum and magnetic moment. This challenge can be addressed by analyzing the flow of energy and charge for the counterexample states. The second argument is an explicit proof (presented in C.-P. Chuu et al. [Solid State Commun. 150, 533 (2010)]) that there is a minimum size for purely positive-frequency electron states. This proof hinges on the assumption of a small spread in momentum space, which is violated by the counterexamples that have been put forward.

中文翻译:

小电子态的可能性

一些作者声称,存在完全由自由狄拉克方程的正频率解组成的电子态的最小尺寸(康普顿半径的量级)。其他作者提出了反对这种主张的反例。本文提出了AJ Bracken和GF Melloy [ J. Phys。A. 32,6127(1999)]旁通对他们的可能性两个参数。第一个是一个古老的论点,由于禁止光速运动,如果电子要具有正确的角动量和磁矩,则它必须大于某个最小尺寸。可以通过分析反例状态的能量和电荷流来解决此难题。第二个论点是一个明确的证明(在C.-P. Chuu中提出等。[固态通讯。 150,533(2010)])存在用于纯粹正频率的电子态的最小尺寸。该证明依赖于动量空间分布很小的假设,而提出的反例违反了这一假设。
更新日期:2020-12-01
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