Noncommutative Geometry for Pedestrians

Abstract

A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An extensive bibliography has been added containing reference to recent review articles as well as to part of the original literature.

Lecture given at the International School of Gravitation, Erice, 28 pages, Latex

References in corpus (47)

• M Theory As A Matrix Model: A Conjecture
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• The quantum structure of spacetime at the Planck scale and quantum fields
• Gravity coupled with matter and foundation of non-commutative geometry
• D-branes and Deformation Quantization
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
• A Universal Action Formula
• The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
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• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
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• Linear connections on matrix geometries
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• A generalized Lichnerowicz formula, the Wodzicki Residue and Gravity
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• Quantum Field Theory on Noncommutative Space-Times and the Persistence of Ultraviolet Divergences
• Linear Connections on Graphs
• Quantum Geometry and the Planck Scale

Cited by in corpus (10)

• Gravity from CFT on $S^N(X)$ CFT: Symmetries and Interactions
• Construction of Gauge Theories on Curved Noncommutative Spacetime
• Nonassociative Snyder phi4 Quantum Field Theory
• UV/IR Mixing in Nonassociative Snyder phi^4 Theory
• On Quantum Nature of Black-Hole Spacetime: A Possible New Source of Intense Radiation
• On Coordinate Transformations in Planar Noncommutative Theories
• D0 Matrix Mechanics: New Fuzzy Solutions at Large N
• On the Quantization of Length in Noncommutative Spaces
• Non-commutative field theory approach to two-dimensional vortex liquid system
• Geometric and topological aspects of Type IIB D-branes