Quantum Field Theory in de Sitter Universe: Ambient Space Formalism

TL;DR

This paper develops a rigorous quantum field theory framework in de Sitter space using ambient space formalism, incorporating group representations, analytic two-point functions, and gauge invariance for various spins.

Contribution

It introduces a novel ambient space formalism for quantum fields in de Sitter space, including the construction of massless fields and their gauge properties, with new results on propagations and super-algebra.

Findings

Massless fields with s ≥ 3 cannot propagate in this formalism.

Quantum massless minimally coupled scalar field constructed on Bunch-Davies vacuum.

Gauge invariance and super-algebra structures identified for specific spins.

Abstract

Quantum field theory in the $4$-dimensional de Sitter space-time is constructed in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the complexified pseudo-Riemannian manifolds. The unitary irreducible representations of de Sitter group and their corresponding Hilbert spaces are reformulated in the ambient space formalism. Defining the creation and annihilation operators, quantum field operators and their corresponding analytic two-point functions for various spin fields have been constructed. The various spin massless fields can be constructed in terms of the massless conformally coupled scalar field in this formalism. Then the quantum massless minimally coupled scalar field operator, for the first time, is also constructed on Bunch-Davies vacuum state which preserve the analyticity. We show that the massless fields with $s \geq 3$ cannot propagate in de Sitter ambient space formalism. The massless gauge invariant field equations for $s=1, \frac{3}{2}, 2$ are studied. The gauge spin-$\frac{3}{2}$ fields satisfy the Grassmannian algebra, and hence provoke one to couple them with the gauge spin-$2$ field and the super-algebra is naturally appeared.