Noncommutative QFT and Renormalization

Abstract

Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to ${\varphi }^3$ models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $\theta$-deformed space and derive noncommutative gauge field actions.

To appear in the proceedings of the Workshop "Noncommutative Geometry in Field and String Theory", Corfu, 2005 (Greece)

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• Quantum Field Theory on Noncommutative Spaces
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• Noncommutative Perturbative Dynamics
• Heat kernel expansion: user's manual
• The Spectral Action Principle
• D-branes and Deformation Quantization
• Gauge Theory on Noncommutative Spaces
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• Noncommutative gauge theory for Poisson manifolds
• Phase structure of non-commutative scalar field theories
• The spectral action for Moyal planes
• Phase diagram and dispersion relation of the non-commutative λϕ^{4} model in d=3
• Non-commutative heat kernel
• Renormalization of the noncommutative phi^3 model through the Kontsevich model
• Trouble with space-like noncommutative field theory
• Numerical Results for U(1) Gauge Theory on 2d and 4d Non-Commutative Spaces
• Generalized Yang-Mills actions from Dirac operator determinants
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Cited by in corpus (16)

• Noncommutative Induced Gauge Theory
• Induced Gauge Theory on a Noncommutative Space
• Noncommutative D=4 gravity coupled to fermions
• On the vacuum states for noncommutative gauge theory
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory
• Noncommutative Induced Gauge Theories on Moyal Spaces
• On space-time noncommutative theories at finite temperature
• Heat Trace Asymptotics on Noncommutative Spaces
• Derivations of the Moyal Algebra and Noncommutative Gauge Theories
• Examples of derivation-based differential calculi related to noncommutative gauge theories
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED
• Strong Field, Noncommutative QED
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Induced Gauge Theory on a Noncommutative Space