We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-$1/2$ particles. To next-to-lowest order in $\hslash$, it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudogauge, the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.

中文翻译：

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通过非局部碰撞从涡度产生自旋极化

我们使用大规模自旋维格纳函数的运动方程推导出玻尔兹曼方程中的碰撞项$1/2$粒子。倒数第二个顺序$\hslash$，它包含一个非局部贡献，负责将轨道转换为自旋角动量。在正确选择伪规范时，能量-动量张量的反对称部分完全来自这种非局部贡献。我们表明碰撞项在全局平衡中消失，因此自旋势等于热涡度。在非相对论极限下，能量-动量和自旋张量的运动方程简化为微极流体流体动力学的众所周知的形式。