The field theory Galilean symmetry, which was introduced in the context of modified gravity, gives a neat way to construct Lorentz-covariant theories of a scalar field, such that the equations of motion contain at most second-order derivatives. Here we extend the analysis to an arbitrary number of scalars, and examine the restrictions imposed by an internal symmetry, focussing in particular on SU(N) and SO(N). This therefore extends the possible gradient terms that may be used to stabilise topological objects such as sigma model lumps.
Padilla, A., Saffin, P. M., & Zhou, S. (2011). Multi-Galileons, solitons, and Derrick’s theorem. Physical Review D, 83(4), https://doi.org/10.1103/PhysRevD.83.045009