Related papers: Non-commutative spaces in physics and mathematics
These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures…
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of…
In this pedagogical mini course the basics of the derivation of the noncommutative structures appearing in string theory are reviewed. First we discuss the well established appearance of the noncommutative Moyal-Weyl star-product in the…
During the last two decades Alain Connes developed Noncommutative Geometry (NCG), which allows to unify two of the basic theories of modern physics: General Relativity (GR) and the Standard Model (SM) of Particle Physics as classical field…
We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild…
Non-Commutative (NC) effects in planar quantum mechanics are investigated. We have constructed a {\it{Master}} model for a noncommutative harmonic oscillator by embedding it in an extended space, following the Batalin-Tyutin \cite{bt}…
We study the formulation of quantum statistical mechanics in noncommutative spaces. We construct microcanonical and canonical ensemble theory in noncommutative spaces. We consider for illustration some basic and important examples in the…
Some aspects of replacing C based physics by C_{n} based physics are discussed. Here C_{n} ={R_{n},I_{n}} where R_{n} and I_{n} are the real and imaginary components of the numbers in C_{n}, and both R_{n} and I_{n}) are sets of length 2n…
This thesis follows two main lines of research, both related to relevant aspects of string theory and its phenomenological/cosmological applications. We study two different generalizations of the integrable SG model to NC geometry, after…
I review results from recent investigations of anomalies in fermion--Yang Mills systems in which basic notions from noncommutative geometry (NCG) where found to naturally appear. The general theme is that derivations of anomalies from…
Various approaches by the author and collaborators to define gravitational fluctuations associated with a noncommutative space are reviewed.
In an on-shell conformal field theory approach, we find indications of a three-bracket structure for target space coordinates in general closed string backgrounds. This generalizes the appearance of noncommutative gauge theories for open…
This is the text of the lecture given by the author in Naples at "Giornata IndAM", June 7, 2005. The lecture is addressed at the general mathematical audience and reviews several topics in deformation theory of associative algebras.
This lecture note surveys the gamma matrices in general dimensions with arbitrary signatures, the study of which is essential to understand the supersymmetry in the corresponding spacetime. The contents supplement the lecture presented by…
In these notes we review the role played by the quantum mechanics and sigma models of symmetric product spaces in the light-cone quantization of quantum field theories, string theory and matrix theory. Lectures given at the Institute for…
This is a short review of the relation between the Reduced Models and Noncommutative Yang-Mills Theories (NCYM) based on the work done in collaboration with J. Ambjorn, J. Nishimura and R. Szabo. Contents: 1.Twisted Eguchi-Kawai model…
We present a general framework for Matrix theory compactified on a quotient space R^n/G, with G a discrete group of Euclidean motions in R^n. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We…
Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004.