Noncommutative Geometry: Fuzzy Spaces, the Groenewold-Moyal Plane ?
@article{Balachandran2006NoncommutativeGF, title={Noncommutative Geometry: Fuzzy Spaces, the Groenewold-Moyal Plane ?}, author={Aiyalam P. Balachandran and Babar Ahmed Qureshi}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2006}, volume={2}, pages={094} }
In this talk, we review the basics concepts of fuzzy physics and quantum field theory on the Groenewold-Moyal Plane as examples of noncommutative spaces in physics. We introduce the basic ideas, and discuss some important results in these fields. At the end we outline some recent developments in the field.
Figures from this paper
3 Citations
Dimensional Reduction of Supersymmetric Gauge Theories
- Physics
- 2009
Main objective of the present dissertation is the investigation for all the possible low energy models which emerge in four dimensions by the dimensional reduction of a gauge theory over multiple…
Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry
- PhysicsSymmetry
- 2013
This work reviews applications of the mathematics of fuzzy super-geometry in the construction of supersymmetric versions of VBS (SVBS) states, and gives a pedagogical introduction of SVBS models and their properties.
Monte-Carlo simulation of the Gaussian BFSS matrix model at large number of dimensions
- Physics, Computer Science
- 2022
A Gaussian approximation to the bosonic part of the BFSS matrix model using Monte Carlo simulations based on Metropolis algorithm reproduces with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase.
References
SHOWING 1-10 OF 69 REFERENCES
An Introduction to Noncommutative Spaces and Their Geometries
- Mathematics
- 1997
Noncommutative Spaces and Algebras of Functions.- Projective Systems of Noncommutative Lattices.- Modules as Bundles.- A Few Elements of K-Theory.- The Spectral Calculus.- Noncommutative Differential…
Elements of Noncommutative Geometry
- Mathematics
- 2000
This volume covers a wide range of topics including sources of noncommutative geometry; fundamentals of noncommutative topology; K-theory and Morita equivalance; noncommutative integrodifferential…
Fermion doubling problem and noncommutative geometry. 2.
- Computer Science
- 2000
This paper brings out its relationship to the Ginsparg-Wilson approach for the fermion doubling problem in discrete field theories based on the fuzzy sphere and its cartesian products.
Remarks on twisted noncommutative quantum field theory
- Mathematics
- 2006
We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation…
Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
- Mathematics, Physics
- 2000
D-Branes in Noncommutative Field Theory
- Physics
- 2005
A mathematical introduction to the classical solutions of noncommutative field theory is presented, with emphasis on how they may be understood as states of D-branes in Type II superstring theory.…
Foundations of Quantum Group Theory
- Mathematics
- 1995
Introduction 1. Definition of Hopf algebras 2. Quasitriangular Hopf algebras 3. Quantum enveloping algebras 4. Matrix quantum groups 5. Quantum random walks and combinatorics 6. Bicrossproduct Hopf…
Noncommutative Manifolds, the Instanton Algebra¶and Isospectral Deformations
- Mathematics
- 2001
Abstract: We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of ℝn. They arise naturally from basic considerations of noncommutative…