论文标题
关于QED和QCD的Heisenberg-Euler有效动作的全订单Landau级结构的注意
Note on all-order Landau-level structures of the Heisenberg-Euler effective actions for QED and QCD
论文作者
论文摘要
我们研究了著名的海森伯格 - 欧拉（HE）在恒定电磁场中编码的Landau级结构。我们首先讨论标量和旋转QED的有效作用，然后将其扩展到协变量恒定的铬磁场中的QCD类似物。我们确定所有兰道水平和Zeeman能量从一环阶从适当的时间表示开始，并在求和机制中以全阶Landau级别的独立贡献来得出Schwinger机制的真空持久性概率。我们发现，旋转QED的磁场催化的Schwinger机制的增强，相反，由于Landau量化的“零点能”，对标量QED的指数抑制更强。对于QCD，我们根据其独特的Zeeman能量确定横向和纵向GLUON模式的离散能级，并明确确认纵向螺旋体和雪松机制中幽灵的贡献之间的取消。我们还讨论了被称为尼尔森 - 伯森不稳定性的扰动gluon激发的不稳定基态。
We investigate the Landau-level structures encoded in the famous Heisenberg-Euler (HE) effective action in constant electromagnetic fields. We first discuss the HE effective actions for scalar and spinor QED, and then extend it to the QCD analogue in the covariantly constant chromo-electromagnetic fields. We identify all the Landau levels and the Zeeman energies starting out from the proper-time representations at the one-loop order, and derive the vacuum persistence probability for the Schwinger mechanism in the summation form over independent contributions of the all-order Landau levels. We find an enhancement of the Schwinger mechanism catalyzed by a magnetic field for spinor QED and, in contrast, a stronger exponential suppression for scalar QED due to the "zero-point energy" of the Landau quantization. For QCD, we identify the discretized energy levels of the transverse and longitudinal gluon modes on the basis of their distinct Zeeman energies, and explicitly confirm the cancellation between the longitudinal-gluon and ghost contributions in the Schwinger mechanism. We also discuss the unstable ground state of the perturbative gluon excitations known as the Nielsen-Olesen instability.
