Isometry invariance of exact correlation functions in various charts of Minkowski and de Sitter spaces

TL;DR

This paper investigates how quantum field theory loop corrections in various patches of Minkowski and de Sitter spaces respect or violate isometry invariance, revealing the role of causality and analyticity in these effects.

Contribution

It demonstrates that loop corrections preserve isometry invariance in certain patches but violate it in others, depending on the space-time region and infrared effects.

Findings

Loop corrections respect isometries in Rindler, past wedge, static, and expanding Poincare patches.

Infrared effects cause isometry violations in the future wedge, contracting Poincare patch, and global de Sitter.

Analyticity and causality are key to understanding invariance preservation or violation.

Abstract

We consider quantum field theory with selfinteractions in various patches of Minkowski and de Sitter space-times. Namely, in Minkowski space-time we consider separately right (left) Rindler wedge, past wedge and future wedge. In de Sitter space-time we consider expanding Poincare patch, static patch, contracting Poincare patch and global de Sitter itself. In all cases we restrict our considerations to the isometry invariant states leading to maximally analytic propagators. We prove that loop corrections in right (left) Rindler wedge, in the past wedge (of Minkowski space-time), in the static patch and in the expanding Poincare patch (of de Sitter space-time) respect the corresponding isometries of the corresponding symmetric space-times. All these facts are related to the causality and analyticity properties of the propagators for the states that we consider. At the same time in the future wedge, in the contracting Poincare patch and in global de Sitter space-time infrared effects violate the isometries.