Comments on Galileons

The recent progress in the study of Galileons, i.e. equations of second order with an action invariant under a Galilean transformation is related to work on 'Universal Field Equations' (Fairlie D B et al 1992 Nucl. Phys. B 373 214-32) which are second order equations arising by an iterative procedure from arbitrary Lagrangians of weight one in their first derivatives. It is pointed out that the Galileon is simply a Kaluza-Klein reduction of a Universal Field Equation. An implicit solution to the equation of motion is presented, and a class of explicit solutions pointed out. The multi-field extensions of both types of equations are derived from a first order formalism, which is simply the substantive derivative of fluid dynamics.