ENERGY-MOMENTUM TENSOR IN SCALAR QED AND THE RENORMALIZATION-GROUP

We consider the renormalization-group equation satisfied by Green's functions of the energy-momentum tensor in scalar QED. We consider the renormalization-group covariance criterion suggested by Collins and show that this criterion (together with certain boundary conditions) when applied at a nontrivial fixed point *(0), e* of the theory uniquely determines an energy-momentum tensor. It is conjectured that this unique energy-momentum tensor may couple to an external gravity. We also consider the renormalization-group criterion in perturbation series in and e2 and show that no energy-momentum tensor exists satisfying this criterion. We consider also an additional form of boundary conditions which determine a unique solution to the renormalization-group criterion. © 1990 The American Physical Society.