Massless scalar field in two-dimensional de Sitter universe

TL;DR

This paper constructs a gauge-invariant quantum field theory for a massless scalar field in two-dimensional de Sitter space, establishing invariant states and conserved charges within an axiomatic framework.

Contribution

It provides a rigorous construction of the invariant Wightman distribution and physical Hilbert space for the massless scalar field in 2D de Sitter space, emphasizing gauge invariance.

Findings

Invariant Wightman distribution derived as zero-mass limit

Vacuum state and physical Hilbert space constructed

Conserved charge generating gauge invariance identified

Abstract

We study the massless minimally coupled scalar field on a two--dimensional de Sitter space-time in the setting of axiomatic quantum field theory. We construct the invariant Wightman distribution obtained as the renormalized zero--mass limit of the massive one. Insisting on gauge invariance of the model we construct a vacuum state and a Hilbert space of physical states which are invariant under the action of the whole de Sitter group. We also present the integral expression of the conserved charge which generates the gauge invariance and propose a definition of dual field.