# QFT on homothetic Killing twist deformed curved spacetimes

September 06, 2010

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.

Keywords:

QFT on non-commutative spaces, QFT on curved spacetimes