相关论文: A tour of noncommutative spectral theories
We survey noncommutative Choquet theory and some of its applications.
This paper is a rudimentary introduction, geared at non-specialists, to how noncommutative field theories arise in physics and their applications to string theory, particle physics and condensed matter systems.
We present a brief review of selected topics in noncommutative field theories ranging from its revival in string theory, its influence on quantum field theories, its possible experimental signatures and ending with some applications in…
Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.
To appear in Encyclopedia of Mathematical Physics, J.-P. Fran\c{c}oise, G. Naber and T.S. Tsou, eds., Elsevier, 2006. The article surveys the modern developments of noncommutative geometry in string theory.
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…
A summary of noncommutative spectral geometry as an approach to unification is presented. The role of the doubling of the algebra, the seeds of quantization and some cosmological implications are briefly discussed.
In this paper, the notion of F-schemes, a "generalization" of schemes, is introduced to cover unitary noncommutative rings.
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
This is a survey on spectral theory of dynamical systems.
We construct a class of noncommutative spectra and give the basic properties of the class of noncommutative spectra.
A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar…
The commuting graph of a non-commutative ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R\setminus Z(R)$ and two vertices $x, y$ are adjacent if and only if $xy = yx$. In this paper, we compute the spectrum…
We study nonmatrix varieties of $\mathbf{k}$-algebras, where $\mathbf{k}$ is a unital commutative ring. Our results extend to this generality known results for the case in which $\mathbf{k}$ is an infinite field. Also, we generalize these…
This is a copy of the talk given at the conference ``Methods in Field Theory'' at Stara Lesna, The Slovak Republic, Sepemeber 22-26, 1997. An introduction to the noncommutative sphere and a summary of the results of articles q-alg/9703038…
In the past 15 years a study of ``noncommutative projective geometry'' has flourished. By using and generalizing techniques of commutative projective geometry, one can study certain noncommutative graded rings and obtain results for which…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and…
We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and…