电磁动力学与旋度非退化SME粒子中的几何输运
Electromagnetic dynamics and geometric transport in spin-nondegenerate SME particles
AI总结：
研究旋度非退化SME粒子的电磁动力学，探讨其在$b_μ$背景下的几何输运特性，揭示不同扇区的环形频率和半径差异，以及非相对论极限下有效各向异性质量的产生。
摘要：
我们研究了源自标准模型扩展中洛伦兹破坏部分的旋度非退化经典粒子模型的电磁动力学，重点研究$b_μ$背景。从类型2相对论拉格朗日量出发，引入最小电磁耦合，并导出与每个扇区相关的精确哈密顿动力学，以规范协变动能动量为变量。修改的色散关系导致速度与动量之间的扇区依赖关系，直接影响对外部场的响应。在均匀磁场存在下，我们显示两个扇区表现出不同的环形频率和半径，暗示即使常数场也能动态解析理论的底层结构。在非相对论极限下，洛伦兹破坏背景诱导了扇区依赖的横向惯性响应修改，可解释为有效各向异性质量。投影到单个扇区后，简化动力学获得非规范的辛结构。运动方程可以写成半经典形式，带有有效动量空间曲率$Ω_{±}$，导致异常速度项和修改的相空间度量。因此，纯电场产生与$q\,\mathbf{E} \times Ω_{±}$成比例的相反横向漂移，产生无须磁场的Hall类电流。
英文摘要：
We investigate the electromagnetic dynamics of spin-nondegenerate classical particle models arising from Lorentz-violating sectors of the Standard-Model Extension, focusing on the $b_μ$ background. Starting from the type-2 relativistic Lagrangian, we introduce minimal electromagnetic coupling and derive the exact Hamiltonian dynamics associated with each sector in terms of the gauge-covariant kinetic momentum. The modified dispersion relation leads to a sector-dependent relation between velocity and momentum, which directly affects the response to external fields. In the presence of a uniform magnetic field, we show that the two sectors exhibit distinct cyclotron frequencies and radii, implying that even constant fields dynamically resolve the underlying structure of the theory. In the nonrelativistic regime, the Lorentz-violating background induces a sector-dependent modification of the transverse inertial response, which can be interpreted as an effective anisotropic mass. After projection onto a single sector, the reduced dynamics acquires a noncanonical symplectic structure. The equations of motion can be written in semiclassical form with an effective momentum space curvature $Ω_{\pm}$, leading to anomalous velocity terms and a modified phase-space measure. As a consequence, a purely electric field generates opposite transverse drifts proportional to $q\,\mathbf{E} \times Ω_{\pm}$, producing a Hall-like current without requiring a magnetic field.
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