  We give a quantum mechanical description of accelerated relativistic
particles in the framework of Coherent States (CS) of the (3+1)-dimensional
conformal group SU(2,2), with the role of accelerations played by special
conformal transformations and with the role of (proper) time translations
played by dilations. The accelerated ground state $\tilde\phi_0$ of first
quantization is a CS of the conformal group. We compute the distribution
function giving the occupation number of each energy level in $\tilde\phi_0$
and, with it, the partition function Z, mean energy E and entropy S, which
resemble that of an "Einstein Solid". An effective temperature T can be
assigned to this "accelerated ensemble" through the thermodynamic expression
dE/dS, which leads to a (non linear) relation between acceleration and
temperature different from Unruh's (linear) formula. Then we construct the
corresponding conformal-SU(2,2)-invariant second quantized theory and its
spontaneous breakdown when selecting Poincar\'e-invariant degenerated
\theta-vacua (namely, coherent states of conformal zero modes). Special
conformal transformations (accelerations) destabilize the Poincar\'e vacuum and
make it to radiate.
