  This is the second of three papers on Conformal General Relativity (CGR). The
conformal group is introduced here as the invariance group of the partial order
of causal events in $n$D spacetime. Its general structure, discrete symmetries
and field representations are described in detail. The spontaneous breakdown of
conformal symmetry is then discussed and the role played by a ghost scalar
field and a physical scalar field in 4D spacetime are evidenced. Kinematic--,
conformal-- and proper--time hyperbolic coordinates are introduced in a
negatively curved Milne spacetime for the purpose of providing three different
but equivalent representations of CGR. The first of these is grounded in a
Riemannian manifold and is manifestly conformal invariant, the second is
grounded in a conformally connected Cartan manifold but its conformal
invariance is hidden, the third is grounded in the Riemannian manifold of the
Milne spacetime and has the formal structure of General Relativity (GR). The
relation between CGR and standard inflationary cosmology is also briefly
discussed. Lastly, in view of the detailed study of Higgs--field dynamics
carried out in the third paper, the action integrals, motion equations and
total energy--momentum tensors of the Higgs field interacting with the dilation
field are described in the three representations mentioned above.
