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Gauge theories on deformed spaces. (English) Zbl 1216.81132

Summary: 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.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
81T13 Yang-Mills and other gauge theories in quantum field theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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