Related papers: Noncommutative Generalization of Wilson Lines
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…
A recently proposed connection between closed string field and an open Wilson line defined on an arbitrary contour is further explored here. We suggest that reparametrization invariance of a Wilson line is the principle which determines the…
This article contains a noncommutative generalization of the topological path lifting problem. Noncommutative geometry has no paths and even points. However there are paths of *-automorphisms. It is proven that paths of *-automorphisms…
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the…
We develop a formalism to realize algebras defined by relations on function spaces. For this porpose we construct the Weyl-ordered star-product and present a method how to calculate star-products with the help of commuting vector fields.…
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.
We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of…
Higher order terms in the effective action of noncommutative gauge theories exhibit generalizations of the *-product (e.g. *' and *-3). These terms do not manifestly respect the noncommutative gauge invariance of the tree level action. In…
The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of…
We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.
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.
Application of the noncommutative geometry to several physical models is considered.
An NQ-manifold is a non-negatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study their properties. The Wilson…
In this note the noncommutative geometry is interpreted as a functor, whose range is a family of the operator algebras. Some examples are given and a program is sketched.
A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…
In this lecture, I put forward conjectures asserting that, in all noncommutative field theories, (1) open Wilson lines and their descendants constitute a complete set of interpolating operators of `noncommutative dipoles', obeying dipole…
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…
The Gelfand - Na\u{i}mark theorem supplies the one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological…
We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…
Differential structure of lattices can be defined if the lattices are treated as models of noncommutative geometry. The detailed construction consists of specifying a generalized Dirac operator and a wedge product. Gauge potential and field…