The problem of the improvement term of the energy-momentum tensor ${\theta }_{\mu \nu }$ in ${\phi }^4$ theory is reconsidered. Renormalization-group methods (due to 't Hooft) with dimensional regularization are used. A unique finite improvement coefficient, depending only on the regulator parameter, is shown to renormalize ${\theta }_{\mu \nu }$. This ${\theta }_{\mu \nu }$ has a soft trace at a fixed point. It coincides with the ${\theta }_{\mu \nu }$ suggested by conformal ideas and by Callan, Coleman, and Jackiw (CCJ), if summation of the perturbation theory divergences is allowed. But order by order, the CCJ ${\theta }_{\mu \nu }$ is finite only up to the three-loop level, and not beyond, even if it is correctly dimensionally regularized.

• Received 14 April 1976

DOI:https://doi.org/10.1103/PhysRevD.14.1965