Elementary particles in a curved space

Abstract

The Fierz-Pauli program is carried out for spin-2 fields in-de Sitter space. A spin-s field is associated with an irreducible representation D(E ₀, s) of the universal covering group of SO(3, 2), with extremal weight (L _{0 5}, L_{1 2}) → (E ₀, s). (L _{0 5} is the time translation operator.) The particular cases D(s+1, s) (s=1, 2,...) are characterized by invariance of the field equations under a gauge group and is for this and other reasons called ‘the massless case’. The Fierz-Pauli program is carried out for s=2, E ₀>3; it fails in the special case E ₀=3 only. The limit, as E ₀ → 3, of the Fierz-Pauli field equation agrees with the linearized form of Einstein's gravitational field equation, with cosmological constant λ=-3ρ. Here ρ is the curvature constant of de Sitter space and the linearization referred to is defined relative to the de Sitter metric.