The Cangemi-Jackiw manifold in high dimensions and symplectic structure

TL;DR

This paper generalizes the Poincare gauge manifold to arbitrary dimensions, introduces a symplectic structure on its cotangent bundle, and explores applications in five-dimensional de Sitter space related to group representations and phase space operators.

Contribution

It extends the concept of Poincare gauge manifolds to higher dimensions and attaches a symplectic structure, with specific applications in five-dimensional space and group representation theory.

Findings

Defined Poincare gauge manifold in arbitrary dimensions

Attached a symplectic structure to the cotangent bundle of G

Derived the central extension of the Aghassi-Roman-Santilli group

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.