# Field Theory on Curved Noncommutative Spacetimes

March 16, 2010

We study classical scalar field theories on noncommutative curved spacetimes.
Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005),
3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative
spacetimes by using (Abelian) Drinfel'd twists and the associated *-products
and *-differential geometry. In particular, we allow for position dependent
noncommutativity and do not restrict ourselves to the Moyal-Weyl deformation.
We construct action functionals for real scalar fields on noncommutative curved
spacetimes, and derive the corresponding deformed wave equations. We provide
explicit examples of deformed Klein-Gordon operators for noncommutative
Minkowski, de Sitter, Schwarzschild and Randall-Sundrum spacetimes, which solve
the noncommutative Einstein equations. We study the construction of deformed
Green's functions and provide a diagrammatic approach for their perturbative
calculation. The leading noncommutative corrections to the Green's functions
for our examples are derived.

open access link
SIGMA 6 (2010), 061, 19 pages

@article{Schenkel:2010sc,
author = "Schenkel, Alexander and Uhlemann, Christoph F.",
title = "{Field Theory on Curved Noncommutative Spacetimes}",
journal = "SIGMA",
volume = "6",
year = "2010",
pages = "061",
doi = "10.3842/SIGMA.2010.061",
eprint = "1003.3190",
archivePrefix = "arXiv",
primaryClass = "hep-th",
SLACcitation = "%%CITATION = ARXIV:1003.3190;%%"
}

Keywords:

QFT on non-commutative spaces, QFT on curved spacetimes