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

The coherent slates associated to the discrete series representations D(E-0, s) of SO(3, 2) are constructed in terms of (spin-)tensor fields on D = 4 anti-de Sitter space. For E-0 > s + 5 the linear space H-E0,s spanned by these states is proved to carry the unitary irreducible representation D(E-0, s). The SO(3, 2)-covariant generalized Fourier transform in this space is exhibited. The quasiclassical properties of the coherent stales are analysed. In particular, these states are shown to be localized on the timelike geodesics of anti-de Sitter space.