Canonical quantization of the covariant fields on de Sitter spacetimes

Abstract

The properties of the covariant quantum fields on de Sitter spacetimes are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the $Sp(2,2)$ group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

41 pages no figures, some typos are corrected

References in corpus (6)

• A Maximally Symmetric Vector Propagator
• The physical meaning of the de Sitter invariants
• Rest frames and relativistic effects on de Sitter spacetimes
• Covariant representations of the de Sitter isometry group
• On the rest and flat limits of the scalar modes on the de Sitter spacetime
• Isometry generators in momentum representation of the Dirac theory on the de Sitter spacetime

Cited by in corpus (5)

• Integral representation of the Feynman propagators of the Dirac fermions on the de Sitter expanding universe
• Propagators of the Dirac fermions on spatially flat FLRW spacetimes
• Time evolution of the free Dirac field in spatially flat FLRW space-times
• Flat limit of the de Sitter QFT in the rest frame vacuum
• Unique fermionic vacuum in de Sitter spacetime from hybrid quantum cosmology