Symmetries of de Sitter Particles and Amplitudes

TL;DR

This paper explores how the symmetries of de Sitter spacetime influence quantum field theory, deriving transformation laws, Ward identities, and showing the connection to flat-space physics in the high-momentum limit.

Contribution

It provides explicit symmetry transformation laws for particles in de Sitter space and connects these to scattering amplitudes and Ward identities.

Findings

Derived explicit transformation laws for de Sitter particle states.

Established Ward identities from spacetime symmetries.

Showed the recovery of Poincaré algebra in the high-momentum limit.

Abstract

We discuss the symmetry aspects of quantum field theory in global four-dimensional de Sitter spacetime linked to $SO(1,4)$ isometries. For the unitary irreducible representations relevant to elementary particles, we obtain explicit transformation laws for the symmetry generators acting on one-particle states in a basis adapted to the $SU(2) \times SU(2)'$ decomposition of the Hilbert space. Using these results, we derive the corresponding Ward identities and demonstrate how global spacetime symmetries constrain de Sitter scattering amplitudes. We show that the Poincar\'e algebra and flat-space Ward identities are recovered in the large-momentum limit.