相关论文: Lectures on Arithmetic Noncommutative Geometry

We discuss a general method of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. Starting from the commuting algebra in the conventional gauge,…

We discuss two concepts of metric and linear connections in noncommutative geometry, applying them to the case of the product of continuous and discrete (two-point) geometry.

These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…

A review is given of some 2-dimensional metrics for which noncommutative versions have been found. They serve partially to illustrate a noncommutative extension of the moving-frame formalism. All of these models suggest that there is an…

I dedicated the volume $2$ of monograph 'Introduction into Noncommutative Algebra' to studying of module over non-commutative algebra.

This is the second part of the revised versions of the notes of three consecutive expository lectures given by Chongying Dong, Haisheng Li and Yi-Zhi Huang in the conference on Monster and vertex operator algebras at the Research Institute…

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.

In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external…

This paper gives a short and historical survey on the theory of pure motives in algebraic geometry and reviews some of the recent developments of this theory in noncommutative geometry. The second part of the paper outlines the new theory…

We describe basic concepts of noncommutative geometry and a general construction extending the familiar duality between ordinary spaces and commutative algebras to a duality between Quotient spaces and Noncommutative algebras. Basic tools…

Traditionally, Hodge structures are associated with complex projective varieties. In my expository lectures I discussed a non-commutative generalization of Hodge structures in deformation quantization and in derived algebraic geometry.

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…

The well known relation between extended supersymmetry and complex geometry in the non-linear sigma-models is reviewed, and some recent developments related to the introduction of the non-anti-commutativity, in the context of the…

This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of…

These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is…

These are the notes accompanying three lectures given by the second author at the Motivic Geometry program at CAS, which aim to give an introduction and an overview of some recent developments in the field of reciprocity sheaves.

These are lecture notes of lectures presented at the 1993 Trieste Summer School, dealing with two classes of two-dimensional field theories, (topological) Yang-Mills theory and the G/G gauged WZW model. The aim of these lectures is to…

In Noncommutative Geometry, as in quantum theory, classically real variables are assumed to correspond to self-adjoint operators. We consider the relaxation of the requirement of self-adjointness to mere symmetry for operators $X_i$ which…

It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry.