A new symmetry of the relativistic wave equation
  In this paper we show that there exists a new symmetry in the relativistic wave equation for a scalar field in arbitrary dimensions. This symmetry is related to redefinitions of the metric tensor which implement a map between non-equivalent manifolds. It is possible to interpret these transformations as a generalization of the conformal transformations. In addition, one can show that this set of manifolds together with the transformation connecting its metrics forms a group. As long as the scalar field dynamics is invariant under these transformations, there immediately appears an ambiguity concerning the definition of the underlying background geometry. 
F. T. Falciano and E. Goulart
gr-qc hep-th