Noncommutative versions of Born-Infeld theory

A new generalization of nonlinear Born-Infeld electrodynamics is proposed. It is inspired by the noncommutative geometry and a new interpretation of gauge theories. The variational principle introduced here leads to quite complicated nonlinear equations, which can be solved numerically in certain cases. The spherically symmetric ansatz is analyzed, and static finite-energy solutions are obtained via numerical integration. Then a pure Higgs sector Lagrangian is introduced by analogy with the non-Abelian Born-Infeld generalization. A spherically symmetric configuration and a time-dependent homogeneous field are investigated and qualitative behavior of solutions are discussed.