Related papers: The mass gap problem for the Yang-Mills Field
The compactification on a torus in $SU(\infty)$ Yang-Mills theory is considered. A special form of the configuration of a gauge field on a torus is examined. The vacuum energy and free energy in the presence of fermions coupled with this…
The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau-De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the…
In terms of a gauge-invariant matrix parametrization of the fields, we give an analysis of how the mass gap could arise in non-Abelian gauge theories in two spatial dimensions.
The well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extra dimension (UED) is generalized to an arbitrary number of spatial extra dimensions through a novel compactification scheme. In this paper, the Riemannian flat based…
The free energy in the weak-coupling phase of two-dimensional Yang-Mills theory on a sphere for SO(N) and Sp(N) is evaluated in the 1/N expansion using the techniques of Gross and Matytsin. Many features of Yang-Mills theory are universal…
We analyze Schr\"odinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two eigenvalues below its essential spectrum we…
It will be described how to uniquely fix the gauge using Coulomb gauge fixing, avoiding the problem of Gribov copies. The fundamental modular domain, which represents a one-to-one representation of the set of gauge invariant degrees of…
The space of Sobolev connections, as it has been introduced for studying the variation of Yang-Mills Lagrangian in the critical dimension $4$, happens not to be weakly sequentially complete in dimension larger than $4$. This is a major…
We consider a restricted four-body problem on the dynamics of a massless particle under the gravitational force produced by three mass points forming an equilateral triangle configuration. We assume that the mass m3 of one primary is very…
We study the Hamiltonian formulation of a gravity model obtained from a Yang--Mills theory for a one-parameter family of (A)dS Lie algebras parametrized by $\alpha$, when the family of algebras is contracted to the Poincar\'e algebra in the…
This is the third part of a four-paper sequence, which establishes the Threshold Conjecture and the Soliton-Bubbling vs.~Scattering Dichotomy for the energy critical hyperbolic Yang--Mills equation in the $(4+1)$-dimensional Minkowski…
Fixing a constant $\lambda>0$, for any parameter $\varepsilon>0$ we study critical points of the Yang--Mills--Higgs energy \[ \mathcal{Y}_{\varepsilon}(\nabla,\Phi) = \int_M \varepsilon^2|F_{\nabla}|^2 + |\nabla\Phi|^2 +…
SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied in (1+1) dimensions using Discretised Light-Cone Quantisation. This theory can be obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction. On the…
Starting with a Dirac operator on a configuration space of $SU(2)$ gauge connections we consider its fluctuations with inner automorphisms. We show that a certain type of twisted inner fluctuations leads to a Dirac operator whose square…
The (1+1)-dimensional SU}(N) Yang-Mills Lagrangian, with bare mass M, and gauge coupling e, naively describes gluons of mass M. In fact, renormalization forces M to infinity. The system is in a confined phase, instead of a Higgs phase. The…
Morse-Smale-Floer homology associates the critical points of the action functional of a classical field theory over a manifold to its homology. We associate to the intersection homology of certain Lagrangian submanifolds of R^4 the critical…
Firstly, we consider Yang-Mills theory on ${\mathbb R}^{3,1}$ with an adjoint Higgs field spontaneously breaking a compact gauge group $G$ to a subgroup $H$, so that the Higgs vacuum manifold forms the coset $G/H$. It is shown that in the…
The low-energy dynamics of five-dimensional Yang-Mills theories compactified on S^1 can be described by a four-dimensional gauge theory coupled to a scalar field in the adjoint representation of the gauge group. Perturbative calculations…
Our goal is to discover possible new 4-dimensional euclidean solutions (instantons) in fundamental SU(2) Yang-Mills-Higgs theory, with a constraint added to prevent collapse of the scale. We show that, most likely, there exists one…
In this talk we consider the mass-deformed Yang-Mills theory in the covariant gauge which is obtained by just adding a gluon mass term to the Yang-Mills theory with the covariant gauge fixing term and the associated Faddeev-Popov ghost…