  In this note, we explicitly compute the vacuum expectation value of the
commutator of scalar fields in a d-dimensional conformal field theory on the
cylinder. We find from explicit calculations that we need smearing not only in
space but also in time to have finite commutators except for those of free
scalar operators. Thus the equal time commutators of the scalar fields are not
well-defined for a non-free conformal field theory, even if which is defined
from the Lagrangian. We also have the commutator for a conformal field theory
on Minkowski space, instead of the cylinder, by taking the small distance
limit.
