Constructing phase space distributions with internal symmetries
Constructing phase space distributions with internal symmetries
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DOI：
10.1103/physrevd.99.056003
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发表时间：
2019-01
影响因子：
5
通讯作者：
N. Mueller;R. Venugopalan
中科院分区：
文献类型：
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作者：
N. Mueller;R. Venugopalan
我们讨论了一个从头算世界线的方法来构建系统的内部对称性相空间分布。从量子场论中的Schwinger-Keldysh真实的时间路径积分出发，我们导出了维格纳相空间分布的最一般的扩展，使其包括了用动态格拉斯曼变量表示的颜色和自旋自由度。相应的刘维分布的有色粒子，服从黄的方程，只有单重态和八重态的分量，而更高的时刻是完全由格拉斯曼代数的约束。相空间动力学对自旋的扩展由Pauli-Lubanski矢量的推广表示;其通过Bargmann-Michel-Telegdi方程的时间演化也遵循基础格拉斯曼坐标的相空间轨迹。我们的结果与自旋和颜色的系统中的刘维尔相空间分布的兴趣领域不同的手征流体，有限温度场理论和极化部分子分布函数。我们还评论的手征异常的自旋粒子的相空间动力学中的作用。
We discuss an ab initio world-line approach to constructing phase space distributions in systems with internal symmetries. Starting from the Schwinger-Keldysh real time path integral in quantum field theory, we derive the most general extension of the Wigner phase space distribution to include color and spin degrees of freedom in terms of dynamical Grassmann variables. The corresponding Liouville distribution for colored particles, which obey Wong's equation, has only singlet and octet components, while higher moments are fully constrained by the Grassmann algebra. The extension of phase space dynamics to spin is represented by a generalization of the Pauli-Lubanski vector; its time evolution via the Bargmann-Michel-Telegdi equation also follows from the phase space trajectories of the underlying Grassmann coordinates. Our results for the Liouville phase space distribution in systems with both spin and color are of interest in fields as diverse as chiral fluids, finite temperature field theory and polarized parton distribution functions. We also comment on the role of the chiral anomaly in the phase space dynamics of spinning particles.