恒定电磁场中的相对论运动
Relativistic Motion in a Constant Electromagnetic Field
摘要：
相对论性带电粒子在恒定电磁场中运动时，其速度四维矢量已得到很好的研究。然而，尽管电磁场和运动方程都是纯实的，但由此产生的4速度似乎是由于复杂的电磁场。这项工作表明，这不是由于使用了某些复杂的形式（例如Clifford代数），而是本质上由于洛伦兹群的$o(3,1)$李代数等价于两个可交换的复$su(2)$代数这一事实。用提升和旋转算子表示复$su(2)$生成器，自然会引入复电磁场。这项工作解决的运动方程不是一个矩阵方程，但作为一个运营商的发展方程的生成元的洛伦兹群。将实演化算子分解为两个可交换的复演化算子，然后直接给出速度4-向量的时间演化，而无需任何中间场的参考。
英文摘要：
For a relativistic charged particle moving in a constant electromagnetic field, its velocity 4-vector has been well studied. However, despite the fact that both the electromagnetic field and the equations of motion are purely real, the resulting 4-velocity is seemingly due to a complex electromagnetic field. This work shows that this is not due to some complex formalism used (such as Clifford algebra) but is intrinsically due to the fact that the $o(3,1)$ Lie algebra of the Lorentz group is equivalent to two commuting complex $su(2)$ algebras. Expressing the complex $su(2)$ generators in terms of the boost and rotation operators then naturally introduces a complex electromagnetic field. This work solves the equation of motion not as a matrix equation, but as an operator evolution equation in terms of the generators of the Lorentz group. The factorization of the real evolution operator into two commuting complex evolution operators then directly gives the time evolution of the velocity 4-vector without any reference to an intermediate field.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
