# Quantum Field Theory on Curved Noncommutative Spacetimes

January 18, 2011

We summarize our recently proposed approach to quantum field theory on
noncommutative curved spacetimes. We make use of the Drinfel'd twist deformed
differential geometry of Julius Wess and his group in order to define an action
functional for a real scalar field on a twist-deformed time-oriented, connected
and globally hyperbolic Lorentzian manifold. The corresponding deformed wave
operator admits unique deformed retarded and advanced Green's operators,
provided we pose a support condition on the deformation. The solution space of
the deformed wave equation is constructed explicitly and can be canonically
equipped with a (weak) symplectic structure. The quantization of the solution
space of the deformed wave equation is performed using *-algebras over the ring
C[[\lambda]]. As a new result we add a proof that there exist symplectic
isomorphisms between the deformed and the undeformed symplectic
R[[\lambda]]-modules. This immediately leads to *-algebra isomorphisms between
the deformed and the formal power series extension of the undeformed quantum
field theory. The consequences of these isomorphisms are discussed.

open access link

PoS(CNCFG2010)029

Keywords:

QFT on non-commutative spaces, QFT on curved spacetimes