Related papers: Noncommutative Yang-Mills-Higgs actions from deriv…
We first extend Generalized Differential Calculus (GDC) to higher structures and create generalized G-invariant bilinear forms. In addition, we also focus on developing generalized 2- and 3-connection theories in the framework of GDC. Then,…
This is a next paper from a sequel devoted to algebraic aspects of Yang-Mills theory. We undertake a study of deformation theory of Yang-Mills algebra YM - a ``universal solution'' of Yang-Mills equation. We compute (cyclic) (co)homology of…
This paper aims to develop a non-commutative geometrical version of the theory of Yang--Mills--Scalar--Matter fields. To accomplish this purpose, we will dualize the geometrical formulation of this theory, in which principal $G$--bundles,…
Discretized nonabelian gauge theories living on finite group spaces G are defined by means of a geometric action \int Tr F \wedge *F. This technique is extended to obtain discrete versions of the Born-Infeld action. The discretizations are…
We consider non(anti)commutative superspace with coordinate dependent deformation parameters $C^{\alpha\beta}$. We show that a chiral ${\cal N}=1/2$ supersymmetry can be defined and that chiral and antichiral superfields are still closed…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
We consider bosons on Euclidean R^4 that are minimally coupled to an external Yang-Mills field. We compute the logarithmically divergent part of the cut-off regularized quantum effective action of this system. We confirm the known result…
We describe an infinite-dimensional Kac-Moody-Virasoro algebra of new hidden symmetries for the self-dual Yang-Mills equations related to conformal transformations of the 4-dimensional base space.
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…
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…
A natural extension of the standard model within non-commutative geometry is presented. The geometry determines its Higgs sector. This determination is fuzzy, but precise enough to be incompatible with experiment.
After a short introduction on the theory of homogeneous algebras we describe the application of this theory to the analysis of the cubic Yang-Mills algebra, the quadratic self-duality algebras, their "super" versions as well as to some…
In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and…
In this review article the construction of first order coordinate differential calculi on finitely generated and finitely related associative algebras are considered and explicit construction of the bimodule of one form over such algebras…
In this paper we consider gauge theories that are relativistic and scale-invariant, and we construct their deformed versions via suitable star products. In particular, the non-commutative structure is controlled by Drinfel'd twists that are…
After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois…
We provide a differential structure on arbitrary cleft extensions $B:=A^{\mathrm{co}H}\subseteq A$ for an $H$-comodule algebra $A$. This is achieved by constructing a covariant calculus on the corresponding crossed product algebra…
The usual action of Yang-Mills theory is given by the quadratic form of curvatures of a principal G bundle defined on four dimensional manifolds. The non-linear generalization which is known as the Born-Infeld action has been given. In this…
Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum…
After an overview of noncommutative differential calculus, we construct parts of it explicitly and explain why this construction agrees with a fuller version obtained from the theory of operads.