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

## TL;DR

This paper generalizes Dirac's 1963 representation of the 3+2 de Sitter group using symplectic transformations and a Jordan map, providing new insights into its structure and physical interpretation.

## Contribution

It introduces a generalized Jordan map based on symplectic transformations to reproduce Dirac's representation of the de Sitter group.

## Key findings

- Reproduction of Dirac's 1963 representation using the generalized Jordan map
- Connection between symplectic transformations and de Sitter group representations
- Physical interpretation of Dirac's representation discussed

## Abstract

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.