Spinor and vector field propagators in the de Sitter universe

Using the method developed previously (Schomblond and Spindel, 1968) for treating the propagators of the scalar field, the authors develop a systematic construction of the propagators associated with spin 1/2 and spin 1. To obtain the spin 1/2 propagators, the Dirac equations are solved in terms of positive and negative frequency solutions. The expressions for the propagators are obtained from these solutions by applying the canonical rules of quantification and satisfy a convolution relation. Likewise, the positive frequency solution, of longitudinal polarization and the solutions of transversal polarization are derived for spin 1 from the Broglie-Proca equations, and explicit expressions for the corresponding propagators are obtained by the canonical rules of quantification.