
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 (HeriotWatt 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 Mtheory, 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.
The Guest Editors
Papers in this Issue:

κMinkowski 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 DoplicherFredenhagenRobertsAmorim 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 SpaceTime: KLoop 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, NonCommutative 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 ]

HigherDimensional 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 NonCommutative 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 2Sphere 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 CP^{n}

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 ]

TranslationInvariant 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 ]

OneLoop Calculations and Detailed Analysis of the Localized NonCommutative 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 ]

