  We present a new non-abelian generalization of the Born-Infeld Lagrangian. It
is based on the observation that the basic quantity defining it is the
generalized volume element, computed as the determinant of a linear combination
of metric and Maxwell tensors. We propose to extend the notion of determinant
to the tensor product of space-time and a matrix representation of the gauge
group. We compute such a Lagrangian explicitly in the case of the SU(2) gauge
group and then explore the properties of static, spherically symmetric
solutions in this model. We have found a one-parameter family of finite energy
solutions. In the last section, the main properties of these solutions are
displayed and discussed.
