爱因斯坦-高斯-博内引力中自旋-1/2粒子的动力学 II：非相对论情形
Dynamics for Spin-$1/2$ Particles in Einstein-Gauss-Bonnet Gravity II: Non-Relativistic Case
- Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）
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AI总结：
本文研究EGB引力中自旋-1/2粒子的非相对论量子动力学，通过Fold-Wouthuysen变换推导有效哈密顿量，揭示自旋进动修正，并应用于黑洞A0620-00以探测高斯-博内耦合。
AI中文摘要：
在这项工作中，我研究了爱因斯坦-高斯-博内（EGB）引力中自旋-1/2粒子的非相对论量子动力学，并建立了高曲率修正、费米子动力学与致密天体现象学之间的直接联系。从静态球对称EGB时空中的狄拉克哈密顿量出发，我们执行Fold-Wouthuysen变换并推导出有效哈密顿量，其中包括相对论动能、引力、自旋-轨道和高曲率贡献。随后利用海森堡方程获得速度、力和自旋的动力学，揭示了平动和自旋输运中显式的EGB修正。特别地，自旋-轨道部分诱导了修正的进动频率，其相对于广义相对论的分数偏差为$\delta_{\Omega}=-4(\xi/M^{2})(M/\rho)^{3}$，为高斯-博内耦合提供了清晰的无量纲特征。通过Ehrenfest定理，我们还建立了量子算符动力学与其半经典引力极限之间的对应关系。作为天体物理应用，我们考虑了恒星质量黑洞A0620-00，并表明自旋进动中约$10^{-3}$至$10^{-4}$的预期相对灵敏度可以探测大约$10^{6}$至$10^{8}\\,{\rm m}^{2}$范围内的高斯-博内耦合，具体取决于轨道半径。这一结果将费米子自旋进动确定为测试具有高曲率修正引力的互补通道，并提供了一个量子力学框架，将修正的引力动力学与强引力区域中的精密现象学联系起来。
英文摘要：
In this work, I investigate the non-relativistic quantum dynamics of spin-1/2 particles in Einstein-Gauss-Bonnet (EGB) gravity and establish a direct connection between higher-curvature corrections, fermionic dynamics, and the phenomenology of compact objects. Starting from the Dirac Hamiltonian in a static, spherically symmetric EGB spacetime, we perform a Fold-Wouthuysen transformation and derive the effective Hamiltonian, including relativistic kinetic, gravitational, spin-orbit, and higher-curvature contributions. Heisenberg equations are then used to obtain the dynamics of velocity, force, and spin, revealing explicit EGB corrections for both translational motion and spin transport. In particular, the spin-orbit sector induces a modified precession frequency whose fractional deviation from general relativity scales as $δ_Ω=-4(ξ/M^{2})(M/ρ)^{3}$, providing a clear dimensionless signature of the Gauss-Bonnet coupling. Through Ehrenfest's theorem, we also establish the correspondence between the dynamics of quantum operators and their semiclassical gravitational limit. As an astrophysical application, we consider the stellar-mass black hole A0620-00 and show that prospective relative sensitivities in spin precession on the order of $10^{-3}$ to $10^{-4}$ can probe Gauss-Bonnet couplings in the range of approximately $10^{6}$ to $10^{8}\,{\rm m}^{2}$, depending on the orbital radius. This result identifies fermionic spin precession as a complementary channel for testing gravity with higher-curvature corrections and provides a quantum-mechanical framework connecting modified gravitational dynamics to precision phenomenology in strong-gravity regimes.
