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
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
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:
where T is the tension of the D-brane.
[edit] References
Born-Infeld theory on arxiv.org
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