  Two kinds of realizations of symmetry on classical domains or the Euclidean
version of AdS space are used to study AdS/CFT correspondence. Mass of free
particles is defined as an AdS group invariant, the Klein-Gordon and Dirac
equations for relativistic particles in the AdS space are set up as a mimic in
the case of Minkowskian space. The bulk-boundary propagator on the AdS space is
given by the Poisson kernel. Theorems on the Poisson kernel guarantee the
existence and sole of the bulk-boundary propagator. The propagator is used to
calculate correlators of the theories that live on the boundary of the AdS
space and show conformal invariance, which is desired by the AdS/CFT
correspondence.
