Born-Infeld action

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.

References

Born-Infeld theory on arxiv.org

Open source encyclopedia content modification information:

Authorship and Review

Open source encyclopedia content provided here is not reviewed directly by PediaView.com. Content is authored by an open community of volunteers and is not produced by or in any way affiliated with PediaView.com.

Usage Guidelines

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article on "Born-Infeld action", which is available in its original form here:

http://en.wikipedia.org/w/index.php?title=Born-Infeld_action

All Wikipedia text is available under the terms of the GNU Free Documentation License. Wikipedia® itself is a registered trademark of the Wikimedia Foundation, Inc.