Department of Physics, National Center for Theoretical Sciences, and Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan.
Phys Rev Lett. 2013 Jun 28;110(26):262301. doi: 10.1103/PhysRevLett.110.262301. Epub 2013 Jun 24.
We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a four-dimensional Euclidean Berry monopole which gives an axial anomaly. By integrating out the zeroth component of the 4-momentum p, we reproduce the previous three-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields (FσρF[over ˜]σρ∼EσBσ). This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions.
我们从处于恒定背景电磁场中的自旋为 1/2 的无质量费米子的维格纳函数出发，推导出一个具有明显洛伦兹协变性的相对论手征动力学方程。该方程包含旋度项和一个四维欧几里得 Berry 磁单极子，它会产生轴向反常。通过对动量 p 的零分量进行积分，我们重现了之前从哈密顿方法推导出的三维结果，以及新推导出的旋度项。相空间连续性方程有一个反常源项，它与电场和磁场的乘积成正比（FσρF[over ˜]σρ∼EσBσ）。这在手征磁效应和涡旋效应、手征反常、Berry 曲率和 Wigner 函数框架中的 Berry 磁单极子的统一解释中提供了一种方法。
