The Cangemi–Jackiw Manifold in High Dimensions and Symplectic Structure
✍ Scribed by L.M. Abreu; A.E. Santana; A.Ribeiro Filho
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 116 KB
- Volume
- 297
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
The notion of Poincaré gauge manifold (G), 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 G is defined for arbitrary dimensions and in the sequence a symplectic structure is attached to T * G. 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. D 1, 2753) is derived as a subgroup of linear transformations in G with six dimensions.