Related papers: Noncommutative Choquet theory: A Survey
We establish the ultra-violet finiteness of various classes of noncommutative gauge theories.
We introduce a framework for coverings of noncommutative spaces. Moreover, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.
The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
We review origins and developments of Noncommutative Potential theory as underpinned by the notion of energy form. Recent and new applications are shown to approximation properties of von Neumann algebras.
We present a definition of and discuss basic properties of cross-ratios over noncommutative skew-fields. A new theorem was added.
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 discuss some properties of noncommutative supersymmetric field theories which do not involve gauge fields. We concentrate on the renormalizability issue of these theories.
The purpose of this paper is to initiate Arakelov theory in a noncommutative setting. More precisely, we are concerned with noncommutative arithmetic surfaces. We introduce a version of arithmetic intersection theory on noncommutative…
We discuss the renormalization properties of noncommutative non-gauge supersymmetric field theories.
This article surveys many aspects of the theory of quandles which algebraically encode the Reidemeister moves. In addition to knot theory, quandles have found applications in other areas which are only mentioned in passing here. The main…
This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
We outline a brief description of non commutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.
We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.
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…
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…
We study almost-forward scattering in the context of usual and non-commutative QED. We study the semi-classical behaviour of particles undergoing this scattering process in the two theories, and show that the shock wave picture, effective…
We introduce a formulation of gauge theory on noncommutative spaces based on the concept of covariant coordinates. Some important examples are discussed in detail. A Seiberg-Witten map is established in all cases.
In this paper we use considerations of non-commutative geometry to deduce a model for QCD interactions. The model also explains within the same theoretical framework hitherto purely phenomenological characteristics of the quarks like their…