Galileon Maps: Inequivalent Coset Constructions for Spacetime Symmetries

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Non-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since their relation involves not only a redefinition of the fields but also a field-dependent change of coordinates. A simple and relevant spacetime symmetry is obtained by the contraction of the 4D conformal group that leads to the Galileon group. In this talk I will analyze two non-linear realizations of this group, focusing in particular on the propagation of signals around non-trivial backgrounds.