Journal
REVIEWS OF MODERN PHYSICS
Volume 73, Issue 4, Pages 977-1029Publisher
AMER PHYSICAL SOC
DOI: 10.1103/RevModPhys.73.977
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This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.
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