A study of a non-Abelian generalization of the Born-Infeld action

A new type of non-Abelian generalization of the Born-Infeld action is proposed, in which the spacetime indices and group indices are combined. The action is manifestly Lorentz and gauge invariant. In its power expansion, the lowest order term is the Yang-Mills action. Solutions of the Euler-Lagrange equation for the SU(2) case are considered and we show that there exists an instanton-like solution which has winding number one and finite action.