  We show how the flat spacetime Galileon field theories (FSGFT) in arbitrary
dimensions can be obtained through a Born-Infeld type structure. This
construction involves a brane metric and non-linear combinations of derivatives
of a scalar field. Our setup gives rise to some Galileon tensors and vectors
useful for the variational analysis which are related to the momentum density
of the probe Lovelock branes floating in a $N$-dimensional flat bulk. We find
further that the Noether currents associated to these Galileon theories may be
written in terms of such tensors.
