Spinor two-point functions and Peierls bracket in de Sitter space

TL;DR

This paper derives spinor two-point functions and Peierls brackets in de Sitter space, providing explicit Green functions and supercommutator expressions for spin-1/2 and spin-3/2 fields using geometric methods.

Contribution

It introduces a geometric approach to compute two-point functions and Peierls brackets for spinor fields in de Sitter space, extending previous methods to higher spins.

Findings

Explicit Feynman and Green functions for spinor fields in de Sitter space.

Formulation of supercommutator and Peierls bracket in two-component-spinor language.

Demonstration of the geometric method's effectiveness for higher-spin fields.

Abstract

This paper studies spinor two-point functions for spin-1/2 and spin-3/2 fields in maximally symmetric spaces such as de Sitter spacetime, by using intrinsic geometric objects. The Feynman, positive- and negative-frequency Green functions are then obtained for these cases, from which we eventually display the supercommutator and the Peierls bracket under such a setting in two-component-spinor language.