Related papers: Non-Commutative Instantons and the Seiberg-Witten …

We present an important contribution to the non-commutative approach to the hydrogen atom to deal with lamb shift corrections. This can be done by studying the Klein-Gordon and Dirac equations in a non-commutative space-time up to…

This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…

We present a powerful method to generate various equations which possess the Lax representations on noncommutative (1+1) and (1+2)-dimensional spaces. The generated equations contain noncommutative integrable equations obtained by using the…

We derive maps relating the currents and energy-momentum tensors in noncommutative (NC) gauge theories with their commutative equivalents. Some uses of these maps are discussed. Especially, in NC electrodynamics, we obtain a generalization…

In this paper, we show that various noncommutative integrable equations can be derived from noncommutative anti-self-dual Yang-Mills equations in the split signature, which include noncommutative versions of Korteweg-de Vries, Non-Linear…

We derive the couplings of noncommutative D-branes to spatially varying Ramond-Ramond fields, extending our earlier results in hep-th/0009101. These couplings are expressed in terms of *n products of operators involving open Wilson lines.…

We write down three kinds of scale transformations {\tt i-iii)} on the noncommutative plane. {\tt i)} is the analogue of standard dilations on the plane, {\tt ii)} is a re-scaling of the noncommutative parameter $\theta$, and {\tt iii)} is…

We investigate Yang-Mills instantons on a 7-dimensional manifold of G_2 holonomy. By proposing a spherically symmetric ansatz for the Yang-Mills connection, we have ordinary differential equations as the reduced instanton equation, and give…

We show that the resolution of moduli space of ideal instantons parameterizes the instantons on non-commutative $\IR^{4}$. This moduli space appears as a Higgs branch of the theory of $k$ $D0$-branes bound to $N$ $D4$-branes by the…

We present a semiclassical calculation of instanton effects in N=4 supersymmetric Yang-Mills theory formulated on R^{3}XS^{1} and also in the N=1 theory obtained by introducing chiral multiplet masses. In the N=4 case, these instanton…

We show that a partition function of topological twisted N=4 Yang-Mills theory is given by Seiberg-Witten invariants on a Riemannian four manifolds under the condition that the sum of Euler number and signature of the four manifolds vanish.…

We briefly report on our recent results regarding the introduction of a notion of a q-quaternion and the construction of instanton solutions of a would-be deformed su(2) Yang-Mills theory on the corresponding SO_q(4)-covariant quantum…

The classical Yang-Mills equations are solved for arbitrary semi-simple gauge groups in the Schwinger-Fock gauge. A new class of SU(N) instantons is presented which are not embeddings of SU(N-1) instantons but have non-trivial SU(N) color…

We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform…

I revisit a basic question about the noncommutative Yang-Mills theory: if it exists or not, or more precisely, whether a nonperturbative formulation exists. As the most promising approach, I consider a formulation based on matrix models. It…

We show that in the perturbative regime defined by the coupling constant, the theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with or without Supersymmetry-- gives an ordinary gauge theory which is, at the quantum…

We study various non-perturbative approaches to the quantization of the Seiberg-Witten curve of ${\cal N}=2$, $SU(2)$ super Yang-Mills theory, which is closely related to the modified Mathieu operator. The first approach is based on the…

Instantons in massless theories do not carry over to massive theories due to Derrick's theorem. This theorem can, however, be circumvented, if a constraint that restricts the scale of the instanton is imposed on the theory. Constrained…

There seems to be close relationship between the moduli space of vortices and the moduli space of instantons, which is not yet clearly understood from a standpoint of the field theory. We clarify the reasons why many similarities are found…

In order to overcome ambiguity problem on identification of mathematical objects in noncommutative theory with physical observables, quantum mechanical system coupled to the NC U(1) gauge field in the noncommutative space is reformulated by…