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arXiv 1702.01233hep-phhep-thnucl-th
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协变手征动力学理论的世界线构造

World-line construction of a covariant chiral kinetic theory

Niklas Mueller, Raju Venugopalan

摘要:

讨论了一种新的计算超相对论重离子碰撞手征磁效应的世界线框架。从量子色动力学有效作用量中的费米子行列式出发,我们明确地展示了它的实部如何可以表示为背景场中自旋的、有色的、格拉斯曼粒子的超对称世界线作用量。为了简单起见,我们限制自己的自旋粒子,我们证明了他们的约束哈密顿动力学产生的无质量和有质量的粒子。在半经典极限下,这导致了Bargmann-Michel-Telegdi方程的协变推广;相应的有色粒子的Wong方程的推导是简单的。在前一封信中,我们概述了贝里相如何在大质量粒子的非相对论绝热极限中出现。我们把这里的讨论扩展到具有有限化学势的系统。我们讨论了一个路径积分制定的相对相位的费米子行列式,把它放在同一个立足点的实部。我们构造了相应的反常世界线轴向矢量流,并详细说明了手征反常是如何出现的。我们的工作提供了一个系统的框架,手征费米子的相对论动力学理论在起伏的拓扑背景下,产生CME的退禁闭夸克-胶子等离子体。我们概述了这个框架在多体系统中的一些进一步的应用。

英文摘要:

We discuss a novel world-line framework for computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. Starting from the fermion determinant in the QCD effective action, we show explicitly how its real part can be expressed as a supersymmetric world-line action of spinning, colored, Grassmanian particles in background fields. Restricting ourselves for simplicity to spinning particles, we demonstrate how their constrained Hamiltonian dynamics arises for both massless and massive particles. In a semi-classical limit, this gives rise to the covariant generalization of the Bargmann-Michel-Telegdi equation; the derivation of the corresponding Wong equations for colored particles is straightforward. In a previous letter we outlined how Berry's phase arises in a non-relativistic adiabatic limit for massive particles. We extend the discussion here to systems with a finite chemical potential. We discuss a path integral formulation of the relative phase in the fermion determinant that places it on the same footing as the real part. We construct the corresponding anomalous world-line axial vector current and show in detail how the chiral anomaly appears. Our work provides a systematic framework for a relativistic kinetic theory of chiral fermions in the fluctuating topological backgrounds that generate the CME in a deconfined quark-gluon plasma. We outline some further applications of this framework in many-body systems.

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