Geometric symmetries of the generalized Born-Infeld equation (Q1584140)

The paper treats the geometric symmetries of the system of the Euler-Lagrange equations for the functional \[ L=1-\sqrt{1-\tfrac{1}{2}\text{ Tr} (F_{\mu\nu}F^{\mu\nu})}. \] The functional \(L\) is assumed to be given in the main fibering \((\mathbb{R}^4,SU(2),M)\). This functional is a generalization of the Born-Infeld functional in nonlinear theory of electromagnetic fields. The author proves the theorem on conditional invariance of the algebra \(\widetilde{AP}\times su(2) \) for the system of Euler-Lagrange equations corresponding to the Lagrangian \(L\).