各向异性自旋轨道相互作用引起的空间离散
Discreteness of Space from Anisotropic Spin-Orbit Interaction
摘要：
各种研究量子引力的方法都认为存在一个最小的可测量长度。为了达到这样的最小长度，可以修改不确定原理、修改色散关系、非对易几何或连续洛伦兹对称性破缺。在本文中，我们提出了最小长度可以通过自旋轨道相互作用自然地获得。我们考虑Dresselhaus各向异性自旋轨道相互作用作为微扰哈密顿量。当应用于粒子时，它意味着抓住这个粒子的空间应该以依赖于粒子质量的单位来量子化。这表明，空间中所有可测量的长度都是量子化的，单位取决于存在的质量和Dresselhaus耦合常数。一方面，这表明了接近桌面实验尺度的空间连续统图像的崩溃，另一方面，它提出了自旋-轨道相互作用是低能尺度下自然导致空间量子化的可能的量子引力效应。
英文摘要：
Various approaches to Quantum Gravity suggest an existence of a minimal measurable length. The cost to have such minimal length could be modified uncertainty principle, modified dispersion relation, non-commutative geometry or breaking of continuous Lorentz symmetry. In this paper, we propose that minimal length can be obtained naturally through spin-orbit interaction. We consider Dresselhaus anisotropic spin-orbit interaction as the perturbative Hamiltonian. When applied to a particle, it implies that the space, which seizes this particle, should be quantized in terms of units that depend on particle's mass. This suggests that all measurable lengths in the space are quantized in units depending on existent mass and the Dresselhaus coupling constant. On one side, this indicates a breakdown of the space continuum picture near the scale of tabletop experiments, and on the other side, it proposes that spin-orbit interaction is a possible quantum gravity effect at low energy scale that leads naturally to space quantization.
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