\(1+3\) -Dimensional dS (dS \(_4\) ) Relativity: The Classical Context

This chapter offers a comprehensive examination of various mathematical aspects pertaining to the \(1+3\) -dimensional de Sitter (dS \(_4\) ) relativity group. The group, represented by SO \(_0(1,4)\) or its universal covering group Sp(2, 2), is thoroughly reviewed, along with its corresponding Lie manifold, Lie algebra, and (co-)adjoint orbits. The latter inherently serve as prime candidates for achieving a phase-space interpretation of classical elementary systems that exist in dS \(_4\) spacetime.