Related papers: Noncommutative Choquet theory: A Survey
These notes aim to give an introduction to a few aspects of noncommutative geometry.
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
It has been proposed that the Poincare and some other symmetries of noncommutative field theories should be twisted. Here we extend this idea to gauge transformations and find that twisted gauge symmetries close for arbitrary gauge group.…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
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…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.
The procedure of nonperturbative quantization \`a la Heisenberg is considered. A few applications, features, perspectives, problems, and so on are considered. The comparison with turbulence modeling is performed.
This paper is a very brief and gentle introduction to non-commutative geometry geared primarily towards physicists and geometers. It starts with a brief historical description of the motivation for non-commutative geometry and then goes on…
We give a detailed overview over known results for (no-)collision of a body with the boundary of its container.
A novel approach to the analysis of a noncommutative Chern--Simons gauge theory with matter coupled in the adjoint representation has been discussed. The analysis is based on a recently proposed closed form Seiberg--Witten map which is…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
We survey the field of nonparametric inference under shape constraints, providing a historical overview and a perspective on its current state. An outlook and some open problems offer thoughts on future directions.
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
We continue the investigation of noncommutative cumulants. In this paper various characterizations of noncommutative Gaussian random variables are proved.
We discuss some aspects of noncommutative quantum field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. General properties of these theories are studied as well as the…