Algebraic construction of twinlike models

If the generalized dynamics of K field theories (i.e., field theories with a nonstandard kinetic term) is taken into account, then the possibility of so-called twinlike models opens up, that is, of different field theories which share the same topological defect solution with the same energy density. These twinlike models were first introduced in [M. Andrews, M. Lewandowski, M. Trodden, and D. Wesley, Phys. Rev. D 82, 105006 (2010)], where the authors also considered possible cosmological implications and gave a geometric characterization of twinlike models. A further analysis of the twinlike models was accomplished in [D. Bazeia, J. D. Dantas, A. R. Gomes, L. Losano, and R. Menezes, Phys. Rev. D 84, 045010 (2011)], with the help of the first order formalism, where also the case with gravitational self-interaction was considered. Here we show that by combining the geometric conditions of [M. Andrews, M. Lewandowski, M. Trodden, and D. Wesley, Phys. Rev. D 82, 105006 (2010)], with the first order formalism of [D. Bazeia, J. D. Dantas, A. R. Gomes, L. Losano, and R. Menezes, Phys. Rev. D 84, 045010 (2011)], one may easily derive a purely algebraic method to explicitly calculate an infinite number of twin field theories for a given theory. We determine this algebraic construction for the cases of scalar field theories, supersymmetric scalar field theories, and self-gravitating scalar fields. Further, we give several examples for each of these cases.