# Field redefinitions Sometimes, two different Lagrangians can be related by a field redefinition. This means that they in fact describe the same theory. After all, if we know everything about a particular formulation of a theory, we can then obtain everything of its field-redefined description by a change of variables. Starting from [[0554 Einstein gravity|General Relativity]], for example, we can make a field redefinition$g_{\mu\nu}\to g_{\mu\nu} +c_1 R g_{\mu\nu}+c_2 R_{\mu\nu}.$It is not hard to check that the resulting gravitational Lagrangian at leading order in $c_i$ is given by$R+\lambda_1 R^2+\lambda_2 R^{\mu \nu} R_{\mu \nu},$where $\lambda_i$ is related to $c_i$. This works similarly for fields other than the metric. ## Refs - [[2023#Cohen, Lu, Sutherland]]: field redefinition in an all-loop recursion relation - [[2021#Garousi (Nov)]]: in the presence of a boundary - [[2023#Dong, Remmen, Wang, Weng, Wu]]: two examples of [[0007 RT surface|holographic entanglement entropy]] under field redefinitions