Covariant Quantization of "Massive" Spin-3/2 Fields in the de Sitter Space

TL;DR

This paper develops a covariant quantization method for massive spin-3/2 fields in de Sitter space, utilizing group theory and complex analysis to derive solutions and two-point functions in a curved spacetime context.

Contribution

It introduces a covariant quantization framework for massive spin-3/2 fields in de Sitter space, including explicit solutions, two-point functions, and a coordinate-independent field operator formulation.

Findings

Derived eigenvalue equations for the field in de Sitter space.

Calculated the Wightman two-point function for the field.

Presented a coordinate-independent expression for the field operator.

Abstract

We present a covariant quantization of the free "massive" spin-3/2 fields in four-dimensional de Sitter space-time based on analyticity in the complexified pseudo-Riemannian manifold. The field equation is obtained as an eigenvalue equation of the Casimir operator of the de Sitter group. The solutions are calculated in terms of coordinate-independent de Sitter plane-waves in tube domains and the null curvature limit is discussed. We give the group theoretical content of the field equation. The Wightman two-point function $S^{i \bar j}_{\alpha\alpha'}(x,x')$ is calculated. We introduce the spinor-vector field operator $\Psi_\alpha(f)$ and the Hilbert space structure. A coordinate-independent formula for the field operator $\Psi_\alpha(x)$ is also presented.