Showing papers on "AdS/CFT correspondence published in 1966"

De sitter model for elementary particles

Abstract: The idea has recently been proposed of embedding the isometric groups of motion which apply to elementary particles in curved Riemannian manifolds (~). The use of the manifold V 4 with ~inkowskian signature already imposes very sever6 restrictions on the possible isometry groups (2). The simplest possibility is a space-time of constant curvature, and this corresponds to the two de Sitter groups S04.1 and S03.~. Ro~faN and AG~tSSl (~) have investigated and compared the energy spectra of the de Sitter world theories, i.e. regarded as global symmetry groups. On the other hand ~IICKnL and Li3vY (~) have stressed that the only extension of the Poincar4Lie algebra compatible with relativistic invariance is to the de Sitter algebras. Another interpretation recently proposed (z) showed that if the Wigner-In6nii contraction process is applied simultaneously to S04,1 and SOa,2, unified within the conformal group, then the algebra of quantum mechanics is recovered. The present method adopts a slightly different interpretation. S04.~, called D +, is adopted as the external event space and S03.2, called D-, as the internal structure space, both embedded in V4( + ~--~---). I t will be seen that all points of view are closely related, but this subject will not be investigated here. The use of Das internal structure space is reminiscent of Dirac's original extended particle model (G) for the theory ef the radiating electron. As in his theory the speed of propagation of a light signal inside the particle is greater than c. I t should be noted aIso that the speed of propagation in the external space is less than e, although the difference is locally undetectable. The maximal compact subgroup of S03. ~ is SO a x SO 2 ~ S U 2 • U1, and can therefore be used to label the isospin, I, and hypercharge, Y, quantum numbers. The

Classical Field Theory and Gravitation in a de Sitter World

Abstract: The algebra and the calculus pertaining to a certain class of representations of the de Sitter group is developed. This permits us to formulate covariant field equations in de Sitter space, and, in particular, to construct quantum mechanical equations of motion associated with particles of given spin. The gauge principle is invoked and a spin‐two field emerges, which we identify with the gravitational field. Its coupling to sources is discussed and conservation laws are derived. The emerging nongeometric theory of gravitation is compared with both the Einstein‐Riemann type and other previously proposed nongeometrical theories.