Noncommutative geometry and physics: a review of selected recent results

Abstract

This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry of finite groups, with the explicit example of Z_2, and its application to Kaluza-Klein gauge theories on discrete internal spaces.

Based on lectures given at the TMR School on contemporary string theory and brane physics, Jan 26- Feb 2, 2000, Torino, Italy. To be published in Class. Quant. Grav. 17 (2000). 3 ref.s added, typos corrected, formula on exterior product of n left-invariant one-forms corrected, small changes in the Sect. on integration

References in corpus (10)

• String Theory and Noncommutative Geometry
• Noncommutative Perturbative Dynamics
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Magnetic fields, branes and noncommutative geometry
• Supergravity and Large N Noncommutative Field Theories
• Some Aspects of Deformations of Supersymmetric Field Theories
• Bi-differential calculi and integrable models
• Thermal effects in perturbative noncommutative gauge theories
• Deformation Quantization of Bosonic Strings
• Gravity on Finite Groups

Cited by in corpus (35)

• Non-commutative Oscillators and the commutative limit
• The noncommutative harmonic oscillator in more than one dimensions
• Star Operation in Quantum Mechanics
• Dimensional Reduction over Fuzzy Coset Spaces
• *-TREK: The One-Loop N=4 Noncommutative SYM Action
• Generating All Wigner Functions
• Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems
• Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory
• The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator
• OSp(1|4) supergravity and its noncommutative extension
• Noncommutative Supersymmetric/Integrable Models and String Theory
• Noncommutative gauge and gravity theories and geometric Seiberg-Witten map
• Discretized Yang-Mills and Born-Infeld actions on finite group geometries
• Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle
• Aspects of noncommutative descriptions of planar systems in high magnetic fields
• Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces
• Finite group discretization of Yang-Mills and Einstein actions
• Cosmological Constant and Noncommutativity: A Newtonian point of view
• D-deformed Wess-Zumino model and its renormalizability properties
• Deformed Chern-Simons interaction for nonrelativistic point particles
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Hamiltonian analysis in Lie-Poisson gauge theory
• Twisted SUSY: twisted symmetry versus renormalizability
• Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces
• Two-dimensional Noncommutative atom Gas with Anandan interaction
• A symmetry breaking mechanism by parity assignment in the noncommutative Higgs model
• Cohomological Operators and Covariant Quantum Superalgebras
• Noncommutative de Rham cohomology of finite groups
• Planar field theories with space-dependent noncommutativity
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly
• Flavor structure from misalignment of inner products in noncommutative geometry
• Noncommutative effective theory of vortices in a complex scalar field
• N=1/2 Global SUSY: R-Matrix Approach
• A note on the fuzzy sphere area spectrum, black hole luminosity, and the quantum nature of spacetime
• Chern-Simons supergravities, with a twist