Gauge Theories on Deformed Spaces

Abstract

The aim of this review is to present an overview over available models and approaches to non-commutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold-Moyal spaces and renormalizability, but we will also review other deformations and try to point out common features. This review will by no means be complete and cover all approaches, it rather reflects a highly biased selection.

v2 references added; v3 published version

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• On Non-Commutative U*(1) Gauge Models and Renormalizability
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• Improved Localization of a Renormalizable Non-Commutative Translation Invariant U(1) Gauge Model
• Schwinger functions in noncommutative quantum field theory
• Gauge fields on noncommutative geometries with curvature
• Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences
• Gauge field theories with covariant star-product
• One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model
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Cited by in corpus (16)

• Computing the θ-exact Seiberg-Witten map for arbitrary gauge groups
• A New Approach to Non-Commutative U(N) Gauge Fields
• Yukawa terms in noncommutative SO(10) and E6 GUTs
• On the energy-momentum tensor in Moyal space
• Renormalization on noncommutative torus
• Wong's Equations and Charged Relativistic Particles in Non-Commutative Space
• On the Physics of the Minimal Length: The Question of Gauge Invariance
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• Aspects of perturbative quantum field theory on non-commutative spaces
• Batalin-Vilkovisky quantization of fuzzy field theories
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism
• Quantization of a gauge theory on a curved noncommutative space
• Special Geometries Emerging from Yang-Mills Type Matrix Models
• Field Theory with Coordinate Dependent Noncommutativity
• Extended BRST formulation of a non-commutative U(1) gauge model