ON THE ULTRAVIOLET BEHAVIOR OF QUANTUM FIELDS OVER NONCOMMUTATIVE MANIFOLDS

DOI10.1142/S0217751X99000671zbMath1045.81550arXivhep-th/9804001MaRDI QIDQ4261905

Joseph C. Várilly, José M. Gracia-Bondía

Publication date: 4 October 1999

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9804001

Mathematics Subject Classification ID

Noncommutative geometry methods in quantum field theory (81T75) Geometry of quantum groups (58B32)

Related Items

Probing space–time noncommutativity in the top quark pair production at e⁺e^- collider, Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering, NONLINEAR VACUUM PHENOMENA IN NONCOMMUTATIVE QED, Four-dimensional gravity on a covariant noncommutative space, A short survey of noncommutative geometry, LABORATORY FRAME ANALYSIS OF e⁺e^-→μ⁺μ^- SCATTERING IN THE NONCOMMUTATIVE STANDARD MODEL AT LINEAR COLLIDER, The phase of the scattering matrix, Noncommutative quantum gravity, Perturbative noncommutative quantum gravity, Renormalization of non-commutative U\((N)\) gauge theories, Induced Chern-Simons and WZW action in noncommutative spacetime., Noncommutative field theory and spontaneous symmetry breaking, Diagrams of noncommutative \(\Phi^3\) theory from string theory, Multiloop string amplitudes with \(B\)-field and noncommutative QFT, Perturbative BF-Yang-Mills theory on noncommutative \(\mathbb R^ 4\)., Quantum field theory on noncommutative spaces, Anomalies and Schwinger terms in NCG field theory models, Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions, PERTURBATIVE QUANTUM GAUGE FIELDS ON THE NONCOMMUTATIVE TORUS, Field theories on deformed spaces, Gauge theoretic approach to (ordinary) gravity and its fuzzy extensions in three and four dimensions

Cites Work

• Non-commutative differential geometry
• Current algebras in \(d+1\)-dimensions and determinant bundles over infinite-dimensional Grassmannians
• The action functional in non-commutative geometry
• On the Hopf algebra strucutre of perturbative quantum field theories
• Connes' noncommutative differential geometry and the standard model
• On summability of distributions and spectral geometry
• The local index formula in noncommutative geometry
• Yang-Mills-Higgs versus Connes-Lott
• Principe d'Oka, K-théorie et systèmes dynamiques non commutatifs. (Oka's principle, K-theory and noncommutative dynamical systems)
• Projective Modules over Higher-Dimensional Non-Commutative Tori
• Construction de triplets spectraux à partir de modules de Fredholm
• Quantum electrodynamics in external fields from the spin representation
• Noncommutative integration calculus
• An Algebraic Approach to Quantum Field Theory