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

الأصل · EN

The coherent states associated to the discrete serie representations D(Eₒ,s) of SO(3,2) are constructed in terms of (spin-)tensor fields on D=4 anti-de Sitter space. For Eₒ>s+5 the linear space Hₑₒ,ₛ spanned by these states is proved to carry the unitary irreducible representation D(Eₒ,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.