Euler-Heisenberg Lagrangian

In physics, the Euler–Heisenberg Lagrangian describes the non-linear dynamics of electromagnetic fields in vacuum. It was first obtained by Werner Heisenberg and Hans Heinrich Euler in 1936. By treating the vacuum as a medium, it predicts rates of quantum electrodynamics (QED) light interaction processes.

It takes into account vacuum polarization to one loop, and is valid for electromagnetic fields that change slowly compared to the inverse electron mass:

Here m is the electron mass, e the electron charge, ${\displaystyle {\mathcal {F}}={\frac {1}{2}}\left(\mathbf {B} ^{2}-\mathbf {E} ^{2}\right)}$, and ${\displaystyle {\mathcal {G}}=\mathbf {E} \cdot \mathbf {B} }$.

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