Pauli系统在Lorentz破坏背景下的可积性
The Integrability of Pauli System in Lorentz Violating Background
摘要：
本文在非相对论水平上系统地分析了二维和三维洛伦兹破坏背景下泡利系统的可积性。我们考虑了从所谓的标准模型扩展的QED扇区出发的狄拉克方程的非相对论极限，只保留两种类型的背景耦合，矢量a_mu和轴向矢量b_mu。我们表明，自旋轨道相互作用来作为一个高阶修正的非相对论极限的狄拉克方程。这样的相互作用允许包含自旋度非平凡的，如果允许洛伦兹违反条款，他们可能在特殊情况下是可比的。通过包含所有可能的一阶导数项，并考虑a \ne 0，b \ne 0，和b_0 \ne 0的情形，确定了运动算符常数的可能形式，并讨论了Lorentz破坏背景下可积性的存在性或连续性.
英文摘要：
We systematically analyze the integrability of a Pauli system in Lorentz violating background at the non-relativistic level both in two- and three-dimensions. We consider the non-relativistic limit of the Dirac equation from the QED sector of the so-called Standard Model Extension by keeping only two types of background couplings, the vector a_mu and the axial vector b_mu. We show that the spin-orbit interaction comes as a higher order correction in the non-relativistic limit of the Dirac equation. Such an interaction allows the inclusion of spin degree non-trivially, and if Lorentz violating terms are allowed, they might be comparable under special circumstances. By including all possible first-order derivative terms and considering the cases a\ne 0, b\ne 0, and b_0\ne 0 one at a time, we determine the possible forms of constants of motion operator, and discuss the existence or continuity of integrability due to Lorentz violating background.
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