Quantum Corrections to Stress Tensors and Conformal Invariance

Abstract

Quantum corrections to the energy-momentum tensors of particles are calculated for these theories: (1) scalar electrodynamics, (2) spinor electrodynamics, and (3) scalar particles with $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ self-interaction. It is shown that source theory provides a much more satisfactory approach than conventional means. The primary result of the investigation is the clear establishment of the favored role of the so-called "conformal" stress tensor - that is, the stress tensor that in the zero-mass limit transforms covariantly under the action of the conformal group. In terms of this tensor, unsubtracted spectral forms for the modifications are written down. A heuristic "proof" that this should be generally possible is provided. It is argued that broken scale invariance does not affect this subtraction-free property, and this is confirmed by explicit calculation of the order-${\ensuremath{\lambda}}^{2}$ modifications in the $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ theory.