  The underlying reasons for the difficulty of unitarily implementing the whole
conformal group $SO(4,2)$ in a massless Quantum Field Theory (QFT) are
investigated in this paper. Firstly, we demonstrate that the singular action of
the subgroup of special conformal transformations (SCT), on the standard
Minkowski space $M$, cannot be primarily associated with the vacuum radiation
problems, the reason being more profound and related to the dynamical breakdown
of part of the conformal symmetry (the SCT subgroup, to be more precise) when
representations of null mass are selected inside the representations of the
whole conformal group. Then we show how the vacuum of the massless QFT radiates
under the action of SCT (usually interpreted as transitions to a uniformly
accelerated frame) and we calculate exactly the spectrum of the outgoing
particles, which proves to be a generalization of the Planckian one, this
recovered as a given limit.
