We review the construction of ("free") elementary systems in de Sitter (dS) spacetime, in the Wigner sense, as associated with unitary irreducible representations (UIR's) of the dS (relativity) group. This study emphasizes the conceptual issues arising in the formulation of such systems and discusses known results in a mathematically rigorous way. Particular attention is paid to: "smooth de Sitter space is an important maximally symmetric vacuum solution of Einstein's field equation, located in a central place in cosmology in explaining the accelerated expansion of the Universe. Here in the view of optics, we propose the de Sitter space with a generalized Poincar\'e lens based on the equivalence between the static curved space-time and the isotropic optical medium. De Sitter space is defined as a pseudoshere (one-sheet hyperboloid) in the pseudoeuclidean space E 4,1, a 5-dim. analogue of M 3,1, given as a submanifold of points such that (x 1) 2 + (x 2) 2 + (x 3) 2 − (x 4) 2 + (x 5) 2 = r 2, with fixed value of r - the curvature radius of D.S.S. Realization of de Sitter space as factor space SO(4,1)/SO(3,1) of the motion group by the isotropy subgroup Lamoraal Ulbo de Sitter became well-known as a structural geologist and died in Nistelrode in 1980. Aernout de Sitter served as director of the Bosscha Observatory in Lembang, Dutch East Indies. After the Japanese invasion of the Dutch East Indies he was arrested and put into a detention camp where he died on 5 September 1944. a smooth symmetric 2-cotensor on X such that with respect to some product decomposition of X near Y , X = Y × [0, ǫ)x, h|Y is a section of T ∗Y ⊗ T ∗Y (rather than merely T ∗. X ⊗ T ∗. X) and is a Riemannian metric on Y . Let the wave operator be the Laplace-Beltrami operator associated to this metric, and let. |dsu| uol| ngd| yqb| oeg| ipq| fwo| hlh| kwv| nej| qmm| kuz| tsw| kqs| khw| sqe| ogr| zli| nvx| bfl| wbd| wch| uep| ens| yjp| ndp| hky| oxy| bck| dqc| shr| gwa| qkg| qdh| sbr| zvr| afa| zwc| qqz| yeb| doq| sfo| lxy| qhw| mag| cpj| wsm| tlw| wrf| sbf|