Conformal Energy-Momentum Tensor in Riemannian Space-Time

We consider the scalar field with quartic self-interaction in Riemannian space-time. Identities are proved which connect the modified energy-momentum tensors of Callan, Coleman, and Jackiw in different conformally related space-times. We consider the quantized scalar field in a conformally flat metric, and show that our identities relate the matrix elements of the modified energy-momentum tensor to corresponding matrix elements in Minkowski space. We show further that when the mass can be neglected in the conformal wave equation there is no gravitationally induced particle creation in conformally flat space-times, thus generalizing a result proved earlier in the free-field case. The influence of additional fields and interactions on that result is briefly discussed.