Correspondence between Minkowski and de Sitter Quantum Field Theory

TL;DR

This paper establishes a mathematical correspondence between Klein-Gordon quantum field theories on de Sitter and Minkowski spacetimes, enabling translation of theories across different dimensions and geometries, with potential applications to Anti de Sitter space.

Contribution

It demonstrates a novel dimensional correspondence between QFTs on de Sitter and Minkowski spacetimes, expanding the understanding of quantum fields in curved backgrounds.

Findings

De Sitter QFTs can be derived from Minkowski QFTs in higher dimensions.

Minkowski QFTs satisfying the spectral condition can be expressed as superpositions of de Sitter fields.

The method can be extended to Anti de Sitter spacetime.

Abstract

In this letter we show that the ``preferred'' Klein-Gordon Quantum Field Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition and, conversely, that a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition can be obtained as superposition of d-dimensional de Sitter Klein-Gordon fields in the preferred vacuum. These results establish a correspondence between QFT's living on manifolds having different dimensions. The method exposed here can be applied to study other situations and notably QFT on Anti de Sitter spacetime.