Related papers: Renormalized Quantum Yang-Mills Fields in Curved S…
We address the issue of the all order multiplicative renormalizability of SU(2) Yang-Mills theories quantized in the maximal Abelian gauge in presence of scalar matter fields. The non-linear character of the maximal Abelian gauge requires…
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…
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…
The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The…
In the paper, within the background field method, the renormalization and the gauge dependence is studied as for an SU(2) Yang-Mills theory with multiplets of spinor and scalar fields. By extending the quantum action of the BV-formalism…
Observables of topological Yang-Mills theory were defined by Witten as the classes of an equivariant cohomology. We propose to define them alternatively as the BRST cohomology classes of a superspace version of the theory, where BRST…
We raise the issue whether gauge theories, that are not renormalizable in the usual power-counting sense, are nevertheless renormalizable in the modern sense that all divergences can be cancelled by renormalization of the infinite number of…
We show that pure Yang-Mills theories with Lorentz violation are renormalizable to all orders in perturbation theory. To do this, we employ the algebraic renormalization technique. Specifically, we control the breaking terms with a suitable…
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 formulate the canonical structure of Yang--Mills theory in terms of Poisson brackets of gauge invariant observables analogous to Wilson loops. This algebra is non--trivial and tractable in a light--cone formulation. For U(N) gauge…
We propose a reformulation of Yang-Mills theory as a perturbative deformation of a novel topological (quantum) field theory. We prove that this reformulation of the four-dimensional QCD leads to quark confinement in the sense of area law of…
For a generic gauge-invariant correlator <{\cal Q}[A_{\mu}]>_{A}, we reformulate the standard D=4 Yang-Mills theory as a renormalizable system of two interacting fields a_{\mu} and B_{\mu} which faithfully represent high- and low-energy…
A connection modulo gauge symmetry on the trivial principal bundle $M\times G$ is a morphism from the loop group of $M$ into $G$. Thus, considering only loops around the 2-cells of a distinguished family of progressively refined cellular…
A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be…
The fermionic gyromagnetic ratio g= 2 of the Kerr-Newman spacetime cannot be a computational "coincidence". This naturally immerges in a four dimensional generally covariant modified Yang-Mills action, which depends on the lorentzian…
We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM$_{1+1}$) by operator-algebraic methods. The latter are based on Hamiltonian lattice gauge theory and multi-scale analysis via inductive…
We prove the perturbative renormalisability of pure SU(2) Yang-Mills theory in the abelian gauge supplemented with mass terms. Whereas mass terms for the gauge fields charged under the diagonal U(1) allow to preserve the standard form of…
In the standard formulation of relativistic quantum field theory, a $\mathbb{Z}_2$-graded structure is assumed to realize locality and the boson-fermion dichotomy. While $\mathbb{Z}_2^n$-graded extensions are known to be allowed at the…
The subject of the thesis is the construction of a perturbative quantum theory of interacting fields on a curved space-time, following a point of view pioneered by Stueckelberg and Bogoliubov and developed by Epstein-Glaser on the flat…
Yang-Mills theory in the first order formalism appears as the deformation of a topological field theory, the pure BF theory. In this approach new non local observables are inherited from the topological theory and the operators entering the…