Born-Infeld theory

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In physics, the Born-Infeld theory is a nonlinear generalization of electromagnetism (see nonlinear electrodynamics). We will use the relativistic notation here as this theory is fully relativistic.

The Lagrangian density is

\mathcal{L}=-b^2\sqrt{-\det\left(\eta+{F\over b}\right)}+b^2

where η is the Minkowski metric, F is the Faraday tensor and both are treated as square matrices so that we can take the determinant of their sum; b is a scale parameter. The maximal possible value of the electric field in this theory is b, and the self-energy of point charges is finite. For electric and magnetic fields much smaller than b, the theory reduces to Maxwell electrodynamics.

In 4-dimensional spacetime the Lagrangian can be written as

\mathcal{L}=-b^2\sqrt{1-\frac{E^2-B^2}{b^2}-\frac{(\vec{E}\cdot\vec{B})^2}{b^4}}+b^2

where E is the electric field, and B is the magnetic field.

In string theory, gauge fields on a D-brane (that arise from attached open strings) are described by the same type of Lagrangian:

\mathcal{L}=-T\sqrt{-\det\left(\eta+2\pi\alpha'F\right)}

where T is the tension of the D-brane.

[edit] References

Born-Infeld theory on arxiv.org

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