Solutions of invariant field equations in the (4, 1) de Sitter space

Abstract

Elementary solutions of the invariant scalar, spinor and vector field equations in the (4, 1) de Sitter space are given and their relations to the representation theory of theSO4,1 de Sitter group are pointed out. The solutions obtained for this space-time of constant curvature having curvature radiusR are analogous to the plane-wave solutions in flat Minkowski space-time. They are constructed in terms of the so-called horospheres determining the wave fronts of these de Sitter plane-wave solutions which are characterized by a timelike four-vector ζ(±)μ. For the case of the continuous series of unitary irreducible representations ofSO4,1 the four-vector ζ(±)μ is related to the energy-momentum four-vector ±pμ in the flat-space limitR→∞, and the elementary,i.e. horospherical, solutions in de Sitter space-time go over in this limit into the positive- and negative-frequency plane-wave solutions in Minkowski space-time.