Related papers: Noncommutative Manifolds the Instanton Algebra and…
This work is a continuation of the former paper in which principal bundles are given by compact spin toric manifolds and compact connected semisimple Lie groups. In this paper, ambient manifolds are assumed to be compact toric manifolds and…
Analysis of the covariant theta-exact noncommutative (NC) gauge field theory (GFT), inspired by high energy cosmic rays experiments, is performed in the framework of the inelastic neutrino-nucleon scatterings. Next we have have found…
The main focus of the present work is to study the Feynman's proof of the Maxwell equations using the NC geometry framework. To accomplish this task, we consider two kinds of noncommutativity formulations going along the same lines as…
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…
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic…
We construct U(2) noncommutative multi-instanton solutions by extending Witten's ansatz [1] which reduces the problem of cylindrical symmetry in four dimensions to that of a set of Bogomol'nyi equations for an Abelian Higgsmodel in two…
The 4-dimensional Sklyanin algebra is the homogeneous coordinate ring of a noncommutative analogue of projective 3-space. The degree-two component of the algebra contains a 2-dimensional subspace of central elements. The zero loci of those…
We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analysing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge…
We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on…
We propose a field theoretical model defined on non-commutative space-time with non-constant non-commutativity parameter $\Theta(x)$, which satisfies two main requirements: it is gauge invariant and reproduces in the commutative limit,…
We study the notion of twisted bundles on noncommutative space. Due to the existence of projective operators in the algebra of functions on the noncommutative space, there are twisted bundles with non-constant dimension. The U(1) instanton…
We make some comments on noncommutative $U(N)$-instantons on $\mathbb{R}^4_{\theta}$. We elaborate on the equations for the ASD-connection for free modules. Further we make some remarks on the computation of the topological index of ADHM…
These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…
We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $\nu$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that…
In this Letter we construct the noncommutative (NC) gravity model on the $\theta$-constant NC space-time. We start from the NC $SO(2,3)_\star$ gauge theory and use the enveloping algebra approach and the Seiberg-Witten map to construct the…
We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c manifolds; and conversely, in the presence…
This is my PhD thesis. In this thesis we study the gauge theories on noncommutative Moyal space. We find new static solitons and instantons in terms of the so called generalized Bose operators. Generalized Bose operators are constructed to…
We present a noncommutative extension of Einstein-Hilbert gravity in the context of twist-deformed space-time, with a $\star$-product associated to a quite general triangular Drinfeld twist. In particular the $\star$-product can be chosen…
While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincar\'{e} conjecture (SPC4) for over 30 years, until recently no invariant has existed which could potentially distinguish these examples from…
Using instanton homology with coefficients in $Z/2$ we construct a homomorphism $q_2$ from the homology cobordism group in dimension 3 to the integers which is not a rational linear combination of the instanton $h$--invariant and the…