  The motion of a scalar particle in (d+1)-dimensional AdS space may be
described in terms of the Cartesian coordinates that span the (d+2)-dimensional
space in which the AdS space is embedded. Upon quantization, the mass
hyperboloid defined in terms of the conjugate momenta turns into the wave
equation in AdS space. By interchanging the roles of coordinates and conjugate
momenta in the (d+2)-dimensional space we arrive at a dual description. For
massive modes, the dual description is equivalent to the conventional
formulation, as required by holography. For tachyonic modes, this interchange
of coordinates and momenta establishes a duality between Euclidean AdS and dS
spaces. We discuss its implications on Green functions for the various vacua.
