2004/02/12 by Christian Blohmann
Mathematics · Physics and Astronomy · #math.QA #hep-th #msc:81R60 #msc:17B37
paper · pdf · doi:10.1142/s0217751x04021238
published as Int.J.Mod.Phys. A19 (2004) 5693 · 16 pages; LaTeX
arxiv created 2004/02/12 · arxiv updated 2009/12/01
Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semi-simple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. Using these ordering prescriptions greatly facilitates the construction of invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.