Coherent (spin-)tensor fields on D=4 anti-de Sitter space

The coherent states associated to the discrete serie representations $D(E_o,s)$ of $SO(3,2)$ are constructed in terms of (spin-)tensor fields on $D=4$ anti-de Sitter space. For $E_o>s+5$ the linear space ${\cal H}_{E_o,s}$ spanned by these states is proved to carry the unitary irreducible representation $D(E_o,s)$. The $SO(3,2) $-covariant generalized Fourier transform in this space is exhibited. The quasiclassical properties of the coherent states are analyzed. In particular, these states are shown to be localized on the time-like geodesics of anti-de Sitter space.