Classical and quantum fields in de Sitter space

Abstract

In the (1+4) de Sitter space the equations for free fields of spin 0, spin 1/2 and spin 1 are derived as eigenvalue equations of the Casimir operators. Completeness relations for the solutions are given in the case of spin 0 and spin 1/2, and with these the different Green functions and commutation functions are obtained. It is possible to construct causal commutation functions only for a certain part of the spectrum. This gives rise to a spectrum condition, by which,e.g., the solution satisfying the conformal invariant equation for spin 0 is excluded from the physical state space. All functions are shown to permit an expansion in powers of the de Sitter curvature 1/R, where the first term is in each case the corresponding invariant function of Minkowski space.