Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 062, 70 pages      arXiv:1004.2127
Contribution to the Special Issue “Noncommutative Spaces and Fields”

Gauge Theories on Deformed Spaces

Daniel N. Blaschke a, Erwin Kronberger b, René I.P. Sedmik b and Michael Wohlgenannt b
a) Faculty of Physics, University of Vienna, Boltzmanngasse 5 A-1090 Vienna, Austria
b) Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria

Received April 13, 2010, in final form July 14, 2010; Published online August 04, 2010

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.

Key words: noncommutative geometry; noncommutative field theory; gauge field theories; renormalization.

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