平面波杨-米尔斯背景下的自旋进动与反常偶极耦合
Spin precession and anomalous dipole couplings in a plane-wave Yang-Mills background
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中文总结 AI 辅助
本研究在非阿贝尔平面波杨-米尔斯背景下，利用精确传播子与重整化单圈顶点，推导了反常色磁偶极耦合与自旋-色进动的相关表达式，建立了背景场量与可观测自旋效应的直接联系。
中文摘要 AI 辅助
我们研究了代表非阿贝尔平面波的外杨-米尔斯规范场中的费米子自旋动力学及诱导偶极相互作用。我们采用外规范场中狄拉克方程的精确解、精确费米子格林函数，以及轴规范下重整化的单圈费米子-胶子顶点进行研究。精确传播子会产生与$σ^{μν}F_{μν}^{a} $成正比的自旋相关结构。外场在树图水平通过Bargmann-Michel-Telegdi方程的非阿贝尔推广形式，结合Wong色输运，诱导出自旋进动。精确顶点会产生超出树图水平的相位相关泡利形状因子$F_{2}^{a}\t( 0;φ,φ^{\r}\t) $，其充当反常色磁偶极耦合。对于单色双色非对易平面波，我们推导了诱导泡利系数和反常自旋进动频率的显式弱场表达式。这种情况下的对易子项$gf^{abc}A_{μ}^{b}A_{ν}^{c}$会产生额外的场强分量，以及阿贝尔背景中不存在的动力学诱导进动轴，进而导致耦合的自旋-色进动。我们给出了适用于周期性杨-米尔斯波的、以谐波展开形式表示的精确单圈系数。同时提供了自旋相关振幅、自旋翻转概率和极化不对称性的显式表达式。这些结果建立了强非阿贝尔规范场中精确背景场传播子、重整化顶点函数、反常偶极相互作用与可观测自旋效应之间的直接联系。
英文摘要
We investigate the fermion spin dynamics and induced dipole interactions in an external Yang-Mills gauge field that represents a non-Abelian plane wave. We use the exact solutions of the Dirac equation in the external gauge field, the exact fermion Green's function, and the renormalized one-loop fermion-gluon vertex in the axial gauge. The exact propagator produces spin-dependent structures proportional to $σ^{μν}F_{μν}^{a} $. The external field induces spin precession at tree level through a non-Abelian extension of the Bargmann-Michel-Telegdi equation, coupled with Wong color transport. The exact vertex produces a phase-dependent Pauli form factor $F_{2}^{a}\left( 0;φ,φ^{\prime }\right) $ beyond tree level, which serves as an anomalous chromomagnetic dipole coupling. For monochromatic two-color noncommuting plane waves, explicit weak-field expressions are derived for the induced Pauli coefficient and the anomalous spin-precession frequency. The commutator term $gf^{abc}A_{μ}^{b}A_{ν}^{c}$ in this case, generates additional field-strength components and dynamically induced precession axes not present in Abelian backgrounds, resulting in coupled spin-color precession. The exact one-loop coefficient is provided as a harmonic expansion suitable for periodic Yang-Mills waves. Explicit expressions for spin-dependent amplitudes, spin-flip probabilities, and polarization asymmetries are provided. These results establish a direct connection between exact background-field propagators, renormalized vertex functions, anomalous dipole interactions, and observable spin effects in strong non-Abelian gauge fields.
