Special Issue on Noncommutative Spaces and Fields

The Guest Editors for this special issue are

Paolo Aschieri (E. Fermi Centre, Rome and University Piemonte Orientale, Alessandria, Italy)
Harald Grosse (University of Vienna, Austria)
Giovanni Landi (University of Trieste, Italy)
Richard Szabo (Heriot-Watt University, Edinburgh, United Kingdom)

Over the years, noncommutative geometry has developed into a new branch of pure mathematics, and has also influenced and found applications in many other areas of mathematics. It has been further applied in a variety of physical contexts, most notably to gauge theories, the Standard Model, the fractional quantum Hall effect, string theory and M-theory, and various scenarios for quantum gravity. Quantum field theories on noncommutative spaces have also taught us lessons about foundational issues in field theory and gravity. The aim of this special issue of SIGMA is to provide a contemporary overview of some of the main developments and applications of noncommutative geometry, ranging from formal considerations to phenomenological applications.

The issue contains 31 papers with the total of 783 pages.

We would like to thank all the authors who have published papers in the issue, and to give our special thanks to all the referees for providing constructive reviews.

Papers in this Issue:

κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems

Andrzej Borowiec and Anna Pachol
SIGMA 6 (2010), 086, 31 pages   [ abs   pdf   ps ]

The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space

Everton M.C. Abreu, Albert C.R. Mendes, Wilson Oliveira and Adriano O. Zangirolami
SIGMA 6 (2010), 083, 37 pages   [ abs   pdf   ps ]

A Canonical Trace Associated with Certain Spectral Triples

Sylvie Paycha
SIGMA 6 (2010), 077, 17 pages   [ abs   pdf   ps ]

Snyder Space-Time: K-Loop and Lie Triple System

Florian Girelli
SIGMA 6 (2010), 074, 19 pages   [ abs   pdf   ps ]

Quantum Spacetime: a Disambiguation

Gherardo Piacitelli
SIGMA 6 (2010), 073, 43 pages   [ abs   pdf   ps ]

Measure Theory in Noncommutative Spaces

Steven Lord and Fedor Sukochev
SIGMA 6 (2010), 072, 36 pages   [ abs   pdf   ps ]

Hopf Maps, Lowest Landau Level, and Fuzzy Spheres

Kazuki Hasebe
SIGMA 6 (2010), 071, 42 pages   [ abs   pdf   ps ]

Balanced Metrics and Noncommutative Kähler Geometry

Sergio Lukic
SIGMA 6 (2010), 069, 15 pages   [ abs   pdf   ps ]

Twist Quantization of String and Hopf Algebraic Symmetry

Tsuguhiko Asakawa and Satoshi Watamura
SIGMA 6 (2010), 068, 17 pages   [ abs   pdf   ps ]

Modular Theory, Non-Commutative Geometry and Quantum Gravity

Paolo Bertozzini, Roberto Conti and Wicharn Lewkeeratiyutkul
SIGMA 6 (2010), 067, 47 pages   [ abs   pdf   ps ]

Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

Nicolas Franco
SIGMA 6 (2010), 064, 11 pages   [ abs   pdf   ps ]

Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions

Athanasios Chatzistavrakidis and George Zoupanos
SIGMA 6 (2010), 063, 47 pages   [ abs   pdf   ps ]

Gauge Theories on Deformed Spaces

Daniel N. Blaschke, Erwin Kronberger, René I.P. Sedmik and Michael Wohlgenannt
SIGMA 6 (2010), 062, 70 pages   [ abs   pdf   ps ]

Field Theory on Curved Noncommutative Spacetimes

Alexander Schenkel and Christoph F. Uhlemann
SIGMA 6 (2010), 061, 19 pages   [ abs   pdf   ps ]

Exotic Galilean Symmetry and Non-Commutative Mechanics

Peter A. Horváthy, Luigi Martina and Peter C. Stichel
SIGMA 6 (2010), 060, 26 pages   [ abs   pdf   ps ]

Noncommutativity and Duality through the Symplectic Embedding Formalism

Everton M.C. Abreu, Albert C.R. Mendes and Wilson Oliveira
SIGMA 6 (2010), 059, 36 pages   [ abs   pdf   ps ]

Bifundamental Fuzzy 2-Sphere and Fuzzy Killing Spinors

Horatiu Nastase and Constantinos Papageorgakis
SIGMA 6 (2010), 058, 28 pages   [ abs   pdf   ps ]

A View on Optimal Transport from Noncommutative Geometry

Francesco D'Andrea and Pierre Martinetti
SIGMA 6 (2010), 057, 24 pages   [ abs   pdf   ps ]

A Note on Dirac Operators on the Quantum Punctured Disk

Slawomir Klimek and Matt McBride
SIGMA 6 (2010), 056, 12 pages   [ abs   pdf   ps ]

Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology

Aiyalam P. Balachandran, Alberto Ibort, Giuseppe Marmo and Mario Martone
SIGMA 6 (2010), 052, 22 pages   [ abs   pdf   ps ]

The Multitrace Matrix Model of Scalar Field Theory on Fuzzy CPⁿ

Christian Sämann
SIGMA 6 (2010), 050, 23 pages   [ abs   pdf   ps ]

On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory

Axel de Goursac
SIGMA 6 (2010), 048, 20 pages   [ abs   pdf   ps ]

Translation-Invariant Noncommutative Renormalization

Adrian Tanasa
SIGMA 6 (2010), 047, 13 pages   [ abs   pdf   ps ]

The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation

Bergfinnur Durhuus and Victor Gayral
SIGMA 6 (2010), 046, 17 pages   [ abs   pdf   ps ]

The Noncommutative Ward Metric

Olaf Lechtenfeld and Marco Maceda
SIGMA 6 (2010), 045, 14 pages   [ abs   pdf   ps ]

Discrete Minimal Surface Algebras

Joakim Arnlind and Jens Hoppe
SIGMA 6 (2010), 042, 18 pages   [ abs   pdf   ps ]

Strong Field, Noncommutative QED

Anton Ilderton, Joakim Lundin and Mattias Marklund
SIGMA 6 (2010), 041, 27 pages   [ abs   pdf   ps ]

Integral calculus on E_q(2)

Tomasz Brzeziński
SIGMA 6 (2010), 040, 10 pages   [ abs   pdf   ps ]

One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative p⁻² U(1) Gauge Model

Daniel N. Blaschke, Arnold Rofner and René I.P. Sedmik
SIGMA 6 (2010), 037, 20 pages   [ abs   pdf   ps ]

Emergent Abelian Gauge Fields from Noncommutative Gravity

Allen Stern
SIGMA 6 (2010), 019, 15 pages   [ abs   pdf   ps ]

Quantum Isometry Group for Spectral Triples with Real Structure

Debashish Goswami
SIGMA 6 (2010), 007,  7 pages   [ abs   pdf   ps ]