Related papers: Internal Space for the Noncommutative Geometry Sta…
In string field theory an infinitesimal background deformation is implemented as a canonical transformation whose hamiltonian function is defined by moduli spaces of punctured Riemann surfaces having one special puncture. We show that the…
We report on the following highlights from among the many discoveries made in Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the modular theory for noncommutative tori, 2) Advances on the Baum-Connes…
In this paper we consider the worldsheet of superstring as a noncommutative space. Some additional terms can be added to the superstring action, such that for ordinary worldsheet they are zero. Expansion of this extended action up to the…
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…
We present the construction of the standard model within the framework of non--associative geometry. For the simplest scalar product we get the tree--level predictions $m_W=\frac{1}{2} m_t\,,$ $m_H=\frac{3}{2} m_t$ and $\sin^2 \theta_W=…
Left-right symmetric models are analyzed in the context of noncommutative geometry where we show that spontaneous parity violation is ruled out.
We argue that some features of the standard model, in particular the fermion assignment and symmetry breaking, can be obtained in matrix model which describes noncommutative gauge theory as well as gravity in an emergent way. The mechanism…
In this paper we study the nonlocal effects of noncommutative spacetime on simple physical systems. Our main point is the assumption that the noncommutative effects are consequences of a background field which generates a local spin…
We fully investigate the symmetry breaking patterns occurring upon creation of composite non-Abelian strings: vortex strings in non-Abelian theories where different sets of colours have different amounts of flux. After spontaneous symmetry…
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…
We study an N=1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N=1 superconformal symmetry. The problem is analyzed in…
Noncommutative geometry is based on an idea that an associative algebra can be regarded as "an algebra of functions on a noncommutative space". The major contribution to noncommutative geometry was made by A. Connes, who, in particular,…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
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…
The purely mathematical root of the dequantization constructions is the quest for a sheafification needed for presheaves on a noncommutative space. The moment space is constructed as a commutative space, approximating the noncommutative…
We consider quantization of open string theories in linear dilaton and constant antisymmetric tensor backgrounds and discuss the noncommutativity of space-time coordinates arising in such theories, including their relationship with…
Extensions of the Standard Model of elementary particle physics to noncommutative geometries are proposed by string models. Independent of this motivation, one may consider such a model as an effective field theory with higher-dimensional…
We analyze the perturbative quantization of the spectral action in noncommutative geometry and establish its one-loop renormalizability in a generalized sense, while staying within the spectral framework of noncommutative geometry. Our…
Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…