手征体系中的二级电荷流和应力张量
Second-order Charge Currents and Stress Tensor in Chiral System
摘要：
我们求解了无质量自旋为1/2的带电费米子在整体平衡附近的维格纳方程。在涡量和电磁场的幂展开式中，可以逐阶得到维格纳函数。导出了二阶的维格纳函数，由此可以得到非耗散电荷流和应力张量。电荷密度、能量密度和压力都有来自二阶涡量和电磁场的贡献。在垂直于涡量和二阶电磁场的方向上可以感应出矢量和轴向霍尔电流。我们还发现，在对应力张量进行重正化时，由于电磁场的量子修正，自然会出现迹异常。
英文摘要：
We solve the Wigner equation for massless spin-1/2 charged fermions near global equilibrium. The Wigner function can be obtained order by order in the power expansion of the vorticity and electromagnetic field. The Wigner function has been derived up to the second order from which the non-dissipative charge currents and the stress tensor can be obtained. The charge and energy densities and the pressure have contributions from the vorticity and electromagnetic field at the second order. The vector and axial Hall currents can be induced along the direction orthogonal to the vorticity and electromagnetic field at the second order. We also find that the trace anomaly emerges natually in renormalizing the stress tensor by including the quantum correction from the electromagnetic field.
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