Noncommutative gauge theory for Poisson manifolds

2000/05/12 by Branislav Jurčo, Branislav Jurco, Peter Schupp +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Gauge boson #Gauge fixing #Gauge theory #Introduction to gauge theory #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Pure mathematics #Quantum gauge theory #Supersymmetric gauge theory #Theoretical physics #hep-th #math.QA

paper · pdf · doi:10.1016/s0550-3213(00)00363-1

published as Nucl.Phys.B584:784-794,2000 · 12 pages

arxiv created 2000/05/12 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

Citations

• String theory and noncommutative geometry
• Open strings in background gauge fields
• Noncommutative Yang-Mills from equivalence of star products
• Deformation Quantization of Poisson Manifolds
• Gauge theory on noncommutative spaces
• D-brane field theory on compact spaces
• Choix des signes pour la formalite de M. Kontsevich
• Noncommutative geometry and Matrix theory

Cited by

• Seiberg-Witten maps from the point of view of consistent deformations of gauge theories
• A remark on the deformation of GNS representations of *-algebras