Generalised Jordan map, symplectic transformations and Dirac's representation of the 3 + 2 de Sitter group

In his 1963 paper, Dirac [1] gave `A Remarkable Representation of the 3 + 2 de- Sitter Group’. We reproduce this representation using a generalised Jordan map which is motivated by the infinitesimal symplectic transformations related to the four dimensional symplectic group Sp(4). A physical picture of Dirac’s representation is also discussed.