QFT on homothetic Killing twist deformed curved spacetimes

TL;DR

This paper investigates how quantum field theory on curved spacetimes is affected by a specific type of geometric deformation involving homothetic Killing vectors, revealing a *-algebra isomorphism and implications for localization.

Contribution

It introduces a new class of deformations of QFT on curved spacetimes using homothetic Killing vectors and demonstrates their algebraic equivalence to undeformed theories.

Findings

Deformations deform equations of motion and Green's functions.

Existence of *-algebra isomorphism between deformed and undeformed QFTs.

Noncommutative geometry limits arbitrary spacetime localization.

Abstract

We study the quantum field theory (QFT) of a free, real, massless and curvature coupled scalar field on self-similar symmetric spacetimes, which are deformed by an abelian Drinfel'd twist constructed from a Killing and a homothetic Killing vector field. In contrast to deformations solely by Killing vector fields, such as the Moyal-Weyl Minkowski spacetime, the equation of motion and Green's operators are deformed. We show that there is a *-algebra isomorphism between the QFT on the deformed and the formal power series extension of the QFT on the undeformed spacetime. We study the convergent implementation of our deformations for toy-models. For these models it is found that there is a *-isomorphism between the deformed Weyl algebra and a reduced undeformed Weyl algebra, where certain strongly localized observables are excluded. Thus, our models realize the intuitive physical picture that noncommutative geometry prevents arbitrary localization in spacetime.