Conformal transformations with multiple scalar fields

Many interesting models incorporate scalar fields with nonminimal couplings to the spacetime Ricci curvature scalar. As is well known, if only one scalar field is nonminimally coupled, then one may perform a conformal transformation to a new frame in which both the gravitational portion of the Lagrangian and the kinetic term for the (rescaled) field assume canonical form. We examine under what conditions the gravitational and kinetic terms in the Lagrangian may be brought into canonical form when more than one scalar field has nonminimal coupling. A particular class of two-field models admits such a transformation, but models with more than two nonminimally coupled fields, in general, do not.