THE CONFORMAL SYMMETRY GENERATED BY EQUAL-TIME COMMUTATORS

At the classical level we derive naively from the Ward identity for th e conformal symmetry, treated as a diffeomorphism, the equal-time comm utator between the improved energy-momentum tensor THETA(mn)(y) and th e THETA(k0)(x)-components. The metric field is introduced as an extern al source for the stress tensor. The analysis is done in the weak-fiel d approximation for the metric field. It is further shown that these e qual-time commutators imply the correct conformal symmetry properties for the energy-momentum tensor and the desired algebra of the generato rs for the conformal symmetry group. A simple redefinition of the non- covariant time ordering operator allows to define a <<symmetric>> equa l-time commutator. Our result reproduces an older result obtained some time ago by Schwinger. The investigations are done in an arbitrary d- dimensional Minkowski space.