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arXiv 1305.3133hep-th
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强电磁场下的分数有效Action

Fractional Effective Action at strong electromagnetic fields

Hagen Kleinert, Eckhard Strobel, She-Sheng Xue

摘要:

在1936年,Weisskopf证明了对于消失的电场或磁场,单圈欧拉-海森堡量子电动力学(QED)有效拉格朗日量的强场行为是对数的。在这里,我们推广了洛伦兹不变量\(\vec{E}^2-\vec{B}^2\)和\(\vec{B}\cdot\vec{E}\)的不同限制的结果。对数依赖性可以解释为QED的有效拉格朗日量的反常幂行为的最低阶表现,对于旋量QED具有临界指数\(δ=e^2/(12π)\),对于标量QED具有临界指数\(δ_S=δ/4\)。

英文摘要:

In 1936, Weisskopf showed that for vanishing electric or magnetic fields the strong-field behavior of the one loop Euler-Heisenberg effective Lagrangian of quantum electro dynamics (QED) is logarithmic. Here we generalize this result for different limits of the Lorentz invariants \(\vec{E}^2-\vec{B}^2\) and \(\vec{B}\cdot\vec{E}\). The logarithmic dependence can be interpreted as a lowest-order manifestation of an anomalous power behavior of the effective Lagrangian of QED, with critical exponents \(δ=e^2/(12π)\) for spinor QED, and \(δ_S=δ/4\) for scalar QED.

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