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

TL;DR

This paper derives explicit mode solutions for the Dirac equation in N-dimensional de Sitter space, analyzes their symmetry properties, and provides closed-form expressions for the spinor two-point functions, advancing understanding of quantum fields in curved spacetime.

Contribution

It introduces a method to obtain explicit spinor mode solutions in de Sitter space and derives closed-form two-point functions, enhancing the analytical tools for quantum field theory in curved spacetime.

Findings

Explicit mode solutions for Dirac fields in de Sitter space

Closed-form expressions for massless and massive spinor two-point functions

Analysis of mode transformation properties under de Sitter group

Abstract

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.