Supergravity theories with non-minimal Kähler potentials are characterized by a non-trivial field space manifold with corresponding non-trivial kinetic terms. The scattering amplitudes in these theories can be calculated at fixed background field values by making a field redefinition to Riemann normal coordinates. Because of the Kähler structure of supergravity, a more compact method for calculating amplitudes is obtained by a redefinition to Kähler normal coordinates. We compare both methods and calculate the explicit transformations and amplitudes for several examples in the context of no-scale supergravity with one and two chiral superfields. We show that in all cases the equivalence of the scattering amplitudes using either Riemann normal or Kähler normal coordinates is possible only at extremal points of the scalar potential.

40 pages, 6 Figures