The Cangemi–Jackiw manifold in high dimensions and symplectic structure

Abstract

The notion of Poincaré gauge manifold (View the MathML source), proposed in the context of an (1+1) gravitational theory by D. Cangemi and R. Jackiw (1993, Ann. Phys. (N.Y.)225, 229), is explored from a geometrical point of view. First View the MathML source is defined for arbitrary dimensions and in the sequence a symplectic structure is attached to T*View the MathML source. Treating then the case of five dimensions, a (4, 1) de-Sitter space, applications are presented studing representations of the Poincaré group in association with kinetic theory and the Weyl operators in phase space. The central extension in the Aghassi–Roman–Santilli group (J. J. Aghassi, P. Roman, and R. M. Santilli, 1970, Phys. Rev. D1, 2753) is derived as a subgroup of linear transformations in View the MathML source with six dimensions.