AI 中文总结
该研究推导相对论电子穿过平面波脉冲后的净自旋旋转为联络的完整平行输运，给出与反常磁矩相关的旋转公式，验证了特定条件下的耦合抵消及面积定律，并分析有限聚焦对旋转信号的影响。
AI 中文摘要
我们计算了相对论电子穿过有限持续时间的平面波激光脉冲后留存的自旋旋转。在基于精确g=2演化构建的相互作用绘景中，托马斯-巴格曼-米歇尔-泰莱格迪（Thomas-Bargmann-Michel-Telegdi）方程变为偏振平面上具有常系数联络的平行输运，脉冲仅通过横向矢势在该平面上描绘的闭合曲线进入。净旋转是该联络的完整平行输运（holonomy）：沿传播方向的角度为-1/2 a_e² 𝒜，其中a_e=(g-2)/2为反常磁矩，𝒜为该曲线包围的带符号面积的两倍。该面积是脉冲每单位面积携带的自旋角动量，因此旋转量度了光的螺旋度。将剩余动力学简化为仅通过反常磁矩耦合的旋转是20世纪60年代的精确结果[Ternov, Bagrov, and Klimenko, Sov. Phys. J. 11, 29 (1968); Bagrov and Gitman, The Dirac Equation and its Solutions (De Gruyter, Berlin, 2014), Sec. 5.3]，其给出两种闭式解情况；面积定律是这两种情况界定的一般二阶结果。相同面积决定了中性磁偶极子的取向记忆[Oblak and Seraj, Phys. Rev. D 109, 044037 (2024)]，其耦合量级为1。对于处于Volkov轨道的带电电子，耦合g/2完全抵消，使旋转被抑制1.3×10⁻⁶，留下无g无关部分的通道。我们在180种脉冲构型下验证了g=2时的抵消，在另外89种构型下验证了面积定律。有限聚焦会以1/kw₀的二阶项恢复该部分，除非w₀≳16λ（γ=10时）或270λ（γ=1时），否则该部分会超过反常信号。
英文摘要
We compute the spin rotation that survives after a relativistic electron has crossed a plane-wave laser pulse of finite duration. In the interaction picture built on the exact $g=2$ evolution, the Thomas-Bargmann-Michel-Telegdi equation becomes parallel transport by a connection with constant coefficients on the polarization plane, and the pulse enters only through the closed curve that the transverse vector potential traces there. The net rotation is the holonomy of that connection: an angle $-\frac{1}{2}a_e^2\mathcal{A}$ about the propagation direction, with $a_e=(g-2)/2$ the anomaly and $\mathcal{A}$ twice the signed area enclosed by the curve. That area is the spin angular momentum the pulse carries per unit area, so the rotation measures the helicity of the light. Reduction of the residual dynamics to a rotation coupled through the anomaly alone is an exact result of the 1960s [Ternov, Bagrov, and Klimenko, Sov. Phys. J. 11, 29 (1968); Bagrov and Gitman, The Dirac Equation and its Solutions (De Gruyter, Berlin, 2014), Sec. 5.3], which yields two closed-form cases; the area law is the general second order that those two cases bound. The same area governs the orientation memory of a neutral magnetic dipole [Oblak and Seraj, Phys. Rev. D 109, 044037 (2024)] with a coupling of order unity. For a charged electron on a Volkov orbit the coupling $g/2$ cancels identically, which suppresses the rotation by $1.3\times10^{-6}$ and leaves a channel with no $g$-independent part. We verify the cancellation at $g=2$ over 180 pulse configurations and the area law over 89 more. Finite focusing restores that part at second order in $1/kw_0$, and it exceeds the anomalous signal unless $w_0\gtrsim16λ$ at $γ=10$, or $270λ$ at $γ=1$.
Comments24 pages, 4 figures, 10 tables. Single-file preprint: the article (Secs. I-VIII) followed by its Supplemental Material as an appendix (Secs. S1-S7). Submitted to Physical Review D. Code and data: https://doi.org/10.5281/zenodo.21758393
