On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review

Abstract

When considering quantum field theories on non-commutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe non-commutative scalar field theories on four-dimensional Euclidean Groenewold-Moyal deformed space, also known as `theta-deformed space'. In this work we discuss some major obstacles of constructing a renormalizable non-commutative gauge field model and sketch some possible ways out.

12 pages; v2: references added

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Cited by in corpus (29)

• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Quantum gauge theories on noncommutative 3-d space
• Gauge theories on quantum spaces
• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Gauge Theories on Deformed Spaces
• A New Approach to Non-Commutative U(N) Gauge Fields
• Closed star product on noncommutative ${\mathbb{R}}^3$ and scalar field dynamics
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• Involutive representations of coordinate algebras and quantum spaces
• Gauge fields on noncommutative geometries with curvature
• On Poisson Electrodynamics With Charged Fields
• One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model
• On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED
• Aspects of perturbative quantum field theory on non-commutative spaces
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• Translation-Invariant Noncommutative Renormalization
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Strong Field, Noncommutative QED
• Perturbative effective action for the photon in noncommutative QED${}_2$ and exactness of the Schwinger mass
• One-loop $\beta$ function of noncommutative scalar $QE{D}_4$
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
• Gauge Fields on Non-Commutative Spaces and Renormalization
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories