Born-infeld Lagrangian using Cayley-Dickson algebras

We rewrite the Born-Infeld Lagrangian, which is originally given by the determinant of a 4 x 4 matrix composed of the metric tensor g and the field strength tensor F, using the determinant of a (4.2(n)) x (4.2(n)) matrix H-4.2(n). If the elements of H-4.2(n) are given by the linear combination of g and F, it is found, based on the representation matrix for the multiplication operator of the Cayley-Dickson algebras, that H-4.2(n) is distinguished by a single parameter, where distinguished matrices are not similar matrices. We also give a reasonable condition to fix the parameter.