Fractional Effective Action at strong electromagnetic fields

TL;DR

This paper generalizes the behavior of the Euler-Heisenberg effective Lagrangian in strong electromagnetic fields, revealing a logarithmic dependence linked to anomalous power laws with specific critical exponents in QED.

Contribution

It extends the understanding of the effective Lagrangian's behavior under various Lorentz invariants, identifying a universal logarithmic pattern and associated critical exponents.

Findings

Logarithmic dependence of the effective Lagrangian in different field limits

Identification of critical exponents ^2/(12\u03c0) for spinor QED

Identification of critical exponents ^2/(48c) for scalar QED

Abstract

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 \(\delta=e^2/(12\pi)\) for spinor QED, and \(\delta_S=\delta/4\) for scalar QED.