\(1+1\) -Dimensional dS (dS \(_2\) ) Relativity: The Quantum-Mechanical Context

This chapter delves into the exploration of the construction of (projective) unitary irreducible representations (UIRs) pertaining to the \(1+1\) -dimensional de Sitter (dS \(_2\) ) relativity group. It is highlighted that the (projective) Hilbert spaces hosting these UIRs, in some restricted sense, serve as quantum (“one-particle”) state spaces for elementary systems within the realm of dS \(_2\) .