2007/08/31 by Jean-Christophe Wallet, J-C Wallet
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #BRST quantization #Black Holes and Theoretical Physics #Gauge theory #Hamiltonian lattice gauge theory #Instanton #Introduction to gauge theory #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Supersymmetric gauge theory #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1742-6596/103/1/012007
published as J.Phys.Conf.Ser.103:012007,2008 · 24 pages, 6 figures. Talk given at the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France). References updated. To appear in J. Phys. Conf. Ser
arxiv created 2007/09/26 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative φ 4 -theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed.