A. Boresch et al., THE CONFORMAL SYMMETRY GENERATED BY EQUAL-TIME COMMUTATORS, Nuovo cimento della Società Italiana di Fisica. A. Nuclei, particles and fields, 106(7), 1993, pp. 905-915
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.