can be done for massive gravity by following Arkani-Hamed, Georgi and Schwartz effective field theory for massive gravity. The absence of vDVZ discontinuity in this approach motivated the development of dRGT resummation of massive gravity theory as follows. The interaction potential is built out of the elementary symmetric polynomials of the eigenvalues of the matrices or , parametrized by dimensionless coupling constants or respectively. Here is the matrix square root of the matrix . Written in index notation, is defined by the relation We have introduced a reference metric in order to construct the interaction term. There is a simple reason for this: it is impossible to construct a nontrivial interaction (i.e., nonderivative) term from alone. The only possibilities are and , both of which lead to a cosmological constant term rather than a bona fide interaction. Physically, corresponds to the background metric around which fluctuations take the Fierz–Pauli form. This means that, for instance, nonlinearly completing the Fierz–Pauli theory around Minkowski space given above will lead to dRGT massive gravity with , although the proof of absence of the Boulware–Deser ghost holds for general . The reference metric transforms like a metric tensor under diffeomorphism Therefore , and similar terms with higher powers, transforms as a scalar under the same diffeomorphism. For a change in the coordinates , we expand with such that the perturbed metric becomes: while the potential-like vector transforms according to Stueckelberg trick as such that the Stueckelberg field is defined as . From the diffeomorphism, one can define another Stueckelberg matrix where and have the same eigenvalues. Now, one considers the following symmetries: such that the transformed perturbed metric becomes: The covariant form of these transformations are obtained as follows. If helicity-0 (or spin-0) mode is a pure gauge of unphysical Goldstone modes, with the matrix is a tensor function of the covariantization tensor of the metric perturbation such that tensor is Stueckelbergized by the field . Helicity-0 mode transforms under Galilean transformations , hence the name "Galileons". The matrix is a tensor function of the covariantization tensor of the metric perturbation with components are given by: where is the extrinsic curvature. Interestingly, the covariantization tensor was originally introduced by Maheshwari in a solo authored paper sequel to helicity-() Freund–Maheshwari–Schonberg finite-range gravitation model. In Maheshwari's work, the metric perturbation obeys Hilbert-Lorentz condition under the variation that is introduced in Ogievetsky–Polubarinov massive gravity, where are to