Related papers: The noncommutative geometry of Yang-Mills fields
Cohomological Yang-Mills theory is formulated on a noncommutative differentiable four manifold through the $\theta$-deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the…
The purpose of this article is to apply the concept of the spectral triple, the starting point for the analysis of noncommutative spaces in the sense of A.~Connes, to the case where the algebra $\cA$ contains both bosonic and fermionic…
We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
I will summarize Noncommutative Geometry Spectral Action, an elegant geometrical model valid at unification scale, which offers a purely gravitational explanation of the Standard Model, the most successful phenomenological model of particle…
We consider SU($N$) Yang-Mills theory on ${\mathbb R}^{2,1}\times S^1$, where $S^1$ is a spatial circle. In the infrared limit of a small-circle radius the Yang-Mills action reduces to the action of a sigma model on ${\mathbb R}^{2,1}$…
We show for the case of interacting massless vector bosons, how the structure of Yang-Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a…
In order to have a new perspective on the long-standing problem of the mass gap in Yang-Mills theory, we study the quantum Yang-Mills theory in the presence of topologically nontrivial backgrounds in this paper. The topologically stable…
A class of new nonabelian gauge theories for vector fields on three manifolds is presented. The theories describe a generalization of three-dimensional Yang-Mills theory featuring a novel nonlinear gauge symmetry and field equations for…
The article (Gauge networks in noncommutative geometry, J. Geom. Phys. 75 : 71--91, 2014) that motivates this comment provides, in particular, one answer to the following natural question: what is noncommutative geometry on a lattice? In…
We study pure Yang--Mills theory on $\Sigma\times S^2$, where $\Sigma$ is a compact Riemann surface, and invariance is assumed under rotations of $S^2$. It is well known that the self-duality equations in this set-up reduce to vortex…
We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but embedded into a flat…
We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the…
We lay the foundations of a Morse homology on the space of connections on a principal $G$-bundle over a compact manifold $Y$, based on a newly defined gauge-invariant functional $\mathcal J$. While the critical points of $\mathcal J$…
The maximally supersymmetric Yang-Mills theory in four-dimensional Minkowski space is an exceptional model of mathematical physics. Even more so in the planar limit, where the theory is believed to be integrable. In particular, the…
The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler…
These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate…
In the noncommutative geometry program of Connes there are two variations of the concept of Yang-Mills action functional. We show that for the quantum Heisenberg manifolds they agree.
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying…
There are two notions of Yang-Mills action functional in noncommutative geometry. We show that for noncommutative n-torus both these notions agree. We also prove a structure theorem on the Hermitian structure of a finitely generated…