Super-gauge Field in de Sitter Universe

TL;DR

This paper develops a formalism for massless spin-3/2 fields in de Sitter space, constructing the quantum field operator, Fock space, and two-point functions with de Sitter invariance and conformal properties.

Contribution

It introduces a Gupta-Bleuler triplet framework for vector-spinor gauge fields in de Sitter space and constructs the quantum field operator using polarization states and a conformally coupled scalar.

Findings

Constructed the vector-spinor quantum field operator in de Sitter space.

Derived the de Sitter covariant and analytic two-point function.

Established the invariant space of solutions under de Sitter group representations.

Abstract

The Gupta-Bleuler triplet for vector-spinor gauge field is presented in de Sitter ambient space formalism. The invariant space of field equation solutions is obtained with respect to an indecomposable representation of the de Sitter group. By using the general solution of the massless spin-$\frac{3}{2}$ field equation, the vector-spinor quantum field operator and its corresponding Fock space is constructed. The quantum field operator can be written in terms of the vector-spinor polarization states and a quantum conformally coupled massless scalar field, which is constructed on Bunch-Davies vacuum state. The two-point function is also presented, which is de Sitter covariant and analytic.