A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz–Bargmann-Michel-Telegdi equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties: they are energy conserving, volume conserving, and second-order convergent. These properties are analyzed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. It is demonstrated that the numerical error in a constant magnetic field remains bounded for long-time simulations in contrast to the Boris pusher, whose angular error increases linearly with time. Finally, the intricate spin dynamics of a particle is investigated in a plane-wave field configuration.

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相对论轨迹和自旋动力学的显式体积守恒数值方案

使用贝利斯的克利福德代数表示形式中的洛伦兹-巴格曼-米歇尔-特莱格迪方程，开发了一类显式数值方案来解决相对论动力学和电磁场中粒子的自旋。事实证明，这些数值方法让人联想到跳越法和Verlet方法，它们具有许多重要的特性：它们是能量守恒，体积守恒和二阶收敛。通过在恒定均匀的电动力场中以已知的分析解决方案为基准，对这些属性进行经验分析。事实证明，与鲍里斯推杆不同，对于长时间的仿真，恒定磁场中的数值误差仍然有限，而鲍里斯推杆的角度误差随时间线性增加。最后，