2003/09/30 by Wolfgang Behr, Andreas Sykora
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2004.07.024
published as Nucl.Phys. B698 (2004) 473-502 · 35 pages, v2: references added, v3: PACS added, v4: final version, changes in the order of presentation
openalex publication_date 2004/08/10 · arxiv created 2004/09/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a method where derivations of star-product algebras are used to build covariant derivatives for noncommutative gauge theory. We write down a noncommutative action by linking these derivations to a frame field induced by a nonconstant metric. An example is given where the action reduces in the classical limit to scalar electrodynamics on a curved background. We further use the Seiberg-Witten map to extend the formalism to arbitrary gauge groups. A proof of the existence of the Seiberg-Witten-map for an abelian gauge potential is given for the formality star-product. We also give explicit formulas for the Weyl ordered star-product and its Seiberg-Witten-maps up to second order.