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The Cangemi-Jackiw manifold in high dimensions and symplectic structure

L. M. Abreu·A. E. Santana·A. Ribeiro Filho
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Abstract

The notion of Poincare gauge manifold ($G$), proposed in the context of an (1+1) gravitational theory by Cangemi and Jackiw (D. Cangemi and R. Jackiw, Ann. Phys. (N.Y.) 225 (1993) 229), is explored from a geometrical point of view. First $G$ is defined for arbitrary dimensions, and in the sequence a symplectic structure is attached to $T*G$. Treating the case of five dimensions, a (4,1)-de Sitter space, aplications are presented studing representations of the Poincare 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, Phys. Rev. D 1(1970) 2573) is derived as a subgroup of linear transformations in $G$ with six dimensions.

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L. M. Abreu, A. E. Santana, A. Ribeiro Filho. 2002-01-18. The Cangemi-Jackiw manifold in high dimensions and symplectic structure. https://doi.org/10.1006/aphy.2002.6252

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