Quantum Field Theory in de Sitter space : A survey of recent approaches

TL;DR

This survey reviews recent rigorous methods for quantizing free quantum fields in de Sitter space, highlighting approaches for massive and massless cases based on group representations and analyticity conditions.

Contribution

It compiles and compares recent quantization techniques for free fields in de Sitter space, emphasizing the mathematical frameworks used for different mass regimes.

Findings

Rigorous quantization for massive fields using analyticity of Wightman functions.

Quantization of massless fields employing Gupta-Bleuler-Krein methods.

Clarification of the mathematical structures underlying quantum fields in de Sitter space.

Abstract

We present a survey of rigourous quantization results obtained in recent works on quantum free fields in de Sitter space. For the "massive'' cases which are associated to principal series representations of the de Sitter group SO\_0(1,4), the construction is based on analyticity requirements on the Wightman two-point function. For the "massless'' cases (e.g. minimally coupled or conformal), associated to the discrete series, the quantization schemes are of the Gupta-Bleuler-Krein type.