Spin 1/2 Field Theory in the de Sitter space-time

TL;DR

This paper develops a covariant quantization framework for spin-1/2 fields in 4D de Sitter space, defining two-point functions and field operators with desirable physical properties.

Contribution

It introduces a covariant quantization method for spinor fields in de Sitter space using analyticity, and constructs the associated two-point functions and field operators.

Findings

Defined the Wightman two-point function satisfying key physical conditions.

Established the Hilbert space structure and field operators for spinor fields.

Provided a coordinate-independent expression for the field operator.

Abstract

A covariant quantization of the free spinor fields (s=1/2) in 4-dimensional de Sitter (dS) space-time based on analyticity in the complexified pseudo-Riemanian manifold is presented. We define the Wigthman two-point function ${\cal W}(x,y)$, which satisfies the conditions of: a) positivity, b) locality, c) covariance, and d) normal analyticity. Then the Hilbert space structure and the field operators $\psi (f)$ are defined. A coordinate-independent formula for the unsmeared field operator $\psi (x)$ is also given.