Strict deformations of quantum field theory in de Sitter spacetime

TL;DR

This paper introduces a new deformation method for quantum field theory in de Sitter spacetime using warped convolutions, revealing differences from undeformed theories and connecting to non-commutative Minkowski spacetime in the flat limit.

Contribution

It develops a novel deformation of quantum field theory in de Sitter space via a new Rieffel product and warped convolutions, extending non-commutative geometry techniques.

Findings

Deformed two-point function differs from the undeformed one.

In the flat limit, the deformation reduces to non-commutative Minkowski spacetime.

The deformation is constructed by embedding de Sitter in higher-dimensional Minkowski space.

Abstract

We propose a new deformed Rieffel product for functions in de Sitter spacetime, and study the resulting deformation of quantum field theory in de Sitter using warped convolutions. This deformation is obtained by embedding de Sitter in a higher-dimensional Minkowski spacetime, deforming there using the action of translations and subsequently projecting back to de Sitter. We determine the two-point function of a deformed free scalar quantum field, which differs from the undeformed one, in contrast to the results in deformed Minkowski spacetime where they coincide. Nevertheless, we show that in the limit where de Sitter spacetime becomes flat, we recover the well-known non-commutative Minkowski spacetime.