The eigenmodes for spinor quantum field theory in global de Sitter space-time

The mode solutions of the Dirac equation on N-dimensional de Sitter space-time (dS_{N)) with (N−1)-sphere spatial sections are obtained by analytically continuing the spinor eigenfunctions of the Dirac operator on the N-sphere (S^{N}). The analogs of flat space-time positive frequency modes are identified and a vacuum is defined. The transformation properties of the mode solutions under the de Sitter group double cover (Spin(N,1)) are studied. We reproduce the expression for the massless spinor Wightman two-point function in closed form using the mode-sum method. By using this closed-form expression and taking advantage of the maximal symmetry of dS_{N} we find an analytic expression for the spinor parallel propagator. The latter is used to construct the massive Wightman two-point function in closed form.