Born-Infeld theory

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

:$mathcal\{L\}=-b^2sqrt\{-detleft(eta+\{Fover\; b\}\; ight)\}+b^2$

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

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

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:

:$mathcal\{L\}=-Tsqrt\{-detleft(eta+2pialpha\text{'}F\; ight)\}$

where "T" is the tension of the D-brane.

References

[http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=hep-th&level=2&index1=3228428 Born-Infeld theory on arxiv.org]