\(1+3\) -Dimensional dS (dS \(_4\) ) Relativity: The Quantum Field Theory (QFT) Context

In this chapter, we delve into the development of a consistent formulation for elementary systems living in \(1+3\) -dimensional de Sitter (dS \(_4\) ) spacetime, specifically focusing on the quantum field theory (QFT) level. Our approach combines two essential elements: the symmetry considerations derived from the dS \(_4\) relativity group and its unitary irreducible representations (UIRs) in accordance with the Wigner framework; the utilization of the Wightman–Gärding axioms supplemented with analyticity requirements in the complexified pseudo-Riemannian manifold.