Related papers: Yang-Mills measure on compact surfaces

We show how to formulate Yang-Mills Theory in \m{2+1} dimensions as a hamitonian system within a simplicial regularization and construct its quantization, with special attention to the mass gap. An approximate conformal invariance of the…

Yang--Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P built from the Laplacian and from a first-order differential operator. The…

The 3+1 dimensional Yang-Mills theory with the Pontryagin term included is studied on manifolds with a boundary. Based on the geometry of the universal bundle for Yang-Mills theory, the symplectic structure of this model is exhibited. The…

It is proven that the physical measure for the two-dimensional Yang-Mills theory is purely singular with respect to the kinematical Ashtekar-Lewandowski measure. For this, an explicit decomposition of the gauge orbit space into supports of…

A mathematically rigorous relativistic quantum Yang-Mills theory with an arbitrary semisimple compact gauge Lie group is set up in the Hamiltonian canonical formalism. The theory is non-perturbative, without cut-offs, and agrees with the…

Supersymmetric pure Yang-Mills theory is formulated with a local, i.e. space-time dependent, complex coupling in superspace. Super-Yang-Mills theories with local coupling have an anomaly, which has been first investigated in the Wess-Zumino…

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…

We derive Wong's equations for the finite-dimensional dynamical system representing the motion of a scalar particle on a compact Riemannian manifold with a given free isometric smooth action of a compact semisimple Lie group. The obtained…

We revisit Atiyah and Bott's study of Morse theory for the Yang-Mills functional over a Riemann surface, and establish new formulas for the minimum codimension of a (non-semi-stable) stratum. These results yield the exact connectivity of…

Using the multi-index approach to regularity structures due to F. Otto et al., we construct a regularity structure and a model for it associated to the stochastic Langevin equation for the 3D Euclidean Yang-Mills functional. For the model…

We investigate quantization properties of Hermitian metrics on holomorphic vector bundles over homogeneous compact K\"ahler manifolds. This allows us to study operators on Hilbert function spaces using vector bundles in a new way. We show…

We lay the foundations of a Morse homology on the space of connections on a principal $G$-bundle over a compact manifold $Y$, based on a newly defined gauge-invariant functional $\mathcal J$. While the critical points of $\mathcal J$…

We study isolated singularities of two dimensional Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber space is a compact Riemannian manifold and the structure group is a compact connected Lie group. In general the…

We study the moduli space of Yang--Mills connections on bundles over a conformally compact manifold $\overline{M}$. We prove that, for every Yang--Mills connection $A$ that satisfies an appropriate nondegeneracy condition, and for every…

The Yang-Mills functional integral is studied in an axial variant of 't Hooft's maximal Abelian gauge. In this gauge Gau\ss ' law can be completely resolved resulting in a description in terms of unconstrained variables. Compared to…

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…

Let M be a manifold with Grassmann structure, i.e. with an isomorphism of the cotangent bundle T^*M\cong E\otimes H with the tensor product of two vector bundles E and H. We define the notion of a half-flat connection \nabla^W in a vector…

By making use of the background field method, we derive a novel reformulation of the Yang-Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang-Mills theory with a…

In this paper we revisit the arguments that have led to the proposal of a multi-instanton measure for supersymmetric Yang-Mills theories. We then recall how the moduli space of gauge connections on $\real^4$ can be built from a…

We discuss the construction of the physical configuration space for Yang-Mills quantum mechanics and Yang-Mills theory on a cylinder. We explicitly eliminate the redundant degrees of freedom by either fixing a gauge or introducing gauge…