Deep-Inelastic Electroproduction and Conformal Symmetry

Abstract

Motivated by the observed scale invariance of high-energy inelastic electron-proton scattering, we study the constraints on a Compton amplitude that follow if it is invariant under the full group of conformal coordinate transformations. Although the conformal group contains operations that interchange spacelike and timelike coordinate intervals, a large class of manifestly causal amplitudes can be constructed. We find that the strict application of conformal symmetry reduces the number of independent covariants from four to two in the case of a spin-zero target. The two covariants of the conformal Compton amplitude remain independent when it is restricted to forward scattering. Hence, invariance under the full conformal group yields no constraints on the structure functions of inelastic electron scattering other than that already provided by simple dilation invariance.