Related papers: Quantum Principal Bundles and Yang-Mills-Scalar-Ma…
In this paper we present solutions to the non-commutative geometrical version of the Yang-Mills-Scalar-Matter theory in the Hopf fibration using the $3D$--calculus.
We study quantized Yang-Mills theory with massive vector fields in the framework of causal perturbation theory. The most general form of the interaction which is invariant under operator gauge transformations is pointed out. The generator…
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…
Ordinary-derivative (second-derivative) Lagrangian formulation of classical conformal Yang-Mills field in the (A)dS space of six, eight, and ten dimensions is developed. For such conformal field, we develop two gauge invariant Lagrangian…
In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A…
We make a short review of the formalism that describes Higgs and Yang Mills fields as two particular cases of an appropriate generalization of the notion of connection. We also comment about the several variants of this formalism, their…
The status of several representative gauge theories on various quantum space-times, mainly focusing on Yang-Mills type extensions together with a few matrix model formulations is overviewed. The common building blocks are derivation based…
In our previous publications we have developed some elements of Noncommutative calculus on the enveloping algebras of $A_m$ type, in particular, analogs of the partial derivatives and de Rham complex were defined. Also, we introduced the…
Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…
This set of lecture notes first gives an introduction to the geometry of principal bundles. Next, it demonstrates how they can be used to formalize the concept of gauge theories arising in physics. A basic familiarity with the differential…
Lagrangian classical field theory of even and odd fields is adequately formulated in terms of fibre bundles and graded manifolds. In particular, conventional Yang-Mills gauge theory is theory of connections on smooth principal bundles, but…
The possible actions of symmetry groups on generalized Higgs fields coupled to an Einstein-Yang-Mills field are studied with differential geometrical techniques involving principal and associated bundles. A classification of conjugacy…
In this paper we present original variational formulations of Yang-Mills, Einstein's gravitation and Kaluza-Klein theories, where, in the spirit of General Relativity, the principal bundle structure over the space-time is not fixed a priori…
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…
By considering specific limits in the gauge coupling constant of pure Yang--Mills dynamics, it is shown how there exist topological quantum field theory sectors in such systems defining nonperturbative topological configurations of the…
The purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum principal bundles over non affine bases. We study the quantization of principal bundles G -> G/P, where G is a semisimple group and P a parabolic…
In math.SG/0605587, we studied Yang-Mills functional on the space of connections on a principal G_R-bundle over a closed, connected, nonorientable surface, where G_R is any compact connected Lie group. In this sequel, we generalize the…
We propose a new field-theoretic framework for formulating the non-relativistic quantum mechanics of D particles in a Fock space of U(N) Yang-Mills theories with all different N in a unified way. D-particle field operators, creating and…
This thesis addresses two topics: noncommutative Yang-Mills theories and the AdS/CFT correspondence. In the first part we study a partial summation of the theta-expanded perturbation theory. The latter allows one to define noncommutative…
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…