Geometry and Unitarity of Scalar Fields Coupled to Gravity.

We formulate scalar field theories coupled nonconformally to gravity in a manifestly frame-independent fashion. Physical quantities such as the S matrix should be invariant under field redefinitions, and hence can be represented by the geometry of the target space. This elegant geometric formulation, however, is obscured when considering the coupling to gravity because of the redundancy associated with the Weyl transformation.