相关论文: Large deviations for the Yang-Mills measure on a c…
The vacuum energy is calculated for Yang-Mills (YM) system defined in $D$ dimensional space-time of $S^1\times R^d$ ($D=d+1$), where the possibility of the YM fields to acquire the vacuum expectation values on $S^1$ is taken into account.…
Two numerical schemes are proposed and investigated for the Yang--Mills equations, which can be seen as a nonlinear generalisation of the Maxwell equations set on Lie algebra-valued functions, with similarities to certain formulations of…
We compute the ultraviolet divergences in the self-dual Yang-Mills theory, both in the purely perturbative (zero instanton charge) and topologically non-trivial sectors. It is shown in particular that the instanton measure is precisely the…
In this paper, we prove the local well-posedness of the Yang-Mills system in the Lorenz gauge for initial data in the Besov space $B^\frac12_{2,1}\times B^{-\frac12}_{2,1}$ with additional angular regularity. To the best of our knowledge,…
We calculate the energy of a Yang-Mills vortex as function of its magnetic flux or, else, of the Wilson loop surrounding the vortex center. The calculation is performed in the 1-loop approximation. A parallel with a potential as function of…
Ratios of the true Yang-Mills vacuum wavefunctional, evaluated on any two field configurations out of a finite set of configurations, can be obtained from lattice Monte Carlo simulations. The method was applied some years ago to test…
We establish various existence and uniqueness results for the Yang-Mills flow on cylindrical end 4-manifolds. We also show long-time existence and infinite-time convergence under certain hypotheses on the underlying data.
The large-N limit of the two-dimensional non-local U$(N)$ Yang-Mills theory on an orientable and non-orientable surface with boundaries is studied. For the case which the holonomies of the gauge group on the boundaries are near the…
We consider a vector bundle $E$ over a compact Riemannian manifold $M$=$M^{n}$,$n\geq 4$,and $A$ is a Yang-Mills connection with $L^{\frac{n}{2}}$ curvature $F_{A}$ on $E$.Then we prove a mean value inequality for the density…
There has been some controversies at the large $N$ behaviour of the 2D Yang-Mills and chiral 2D Yang-Mills theories. To be more specific, is there a one parameter family of minima of the free energy in the strong region, or the minimum is…
We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…
Using Hamilton-Jacobi formalism we investigated the massive Yang-Mills theory on both extended and reduced phase-space. The integrability conditions were discussed and the actions were calculated.
The large-group behavior of the nonlocal YM$_2$'s and gYM$_2$'s on a cylinder or a disk is investigated. It is shown that this behavior is similar to that of the corresponding local theory, but with the area of the cylinder replaced by an…
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.
In this paper, we prove the convergence of the discrete Makeenko-Migdal equations for the Yang-Mills model on $(\varepsilon \mathbf{Z})^{2}$ to their continuum counterparts on the plane, in an appropriate sense. The key step in the proof is…
We provide a set of exact solutions of the classical Yang-Mills equations. They have the property to satisfy a massive dispersion relation and hold in all gauges. These solutions can be used to describe the vacuum of the quantum Yang-Mills…
I provide a new idea based on geometric analysis to obtain a positive mass gap in pure non-abelian renormalizable Yang-Mills theory. The orbit space, that is the space of connections of Yang-Mills theory modulo gauge transformations, is…
Models based on Yang-Mills condensate (YMC) have been advocated in the literature and claimed to be successful candidates to explain dark energy. Several instantiations of this simple idea have been considered, the most promising of which…
We consider the motion of a classical colored spinless particle under the influence of an external Yang-Mills potential $A$ on a compact manifold with boundary of dimension $\geq 3$. We show that under suitable convexity assumptions, we can…