Related papers: Notes on the Hamiltonian formulation of 3D Yang-Mi…
The variational approach to the Hamilton formulation of Yang-Mills theory in Coulomb gauge developed by the present authors previously is applied to Yang-Mills theory in 2+1 dimensions and is confronted with the existing lattice data. We…
We show that the Hamiltonian of (N=1;d=10) super Yang-Mills can be expressed as a quadratic form in a very similar manner to that of the (N=4;d=4) theory. We find a similar quadratic form structure for pure Yang-Mills theory but this…
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…
A general method to treat non-Gaussian vacuum wave functionals in the Hamiltonian formulation of a quantum field theory is presented. By means of Dyson--Schwinger techniques, the static Green functions are expressed in terms of the kernels…
We outline a method of relating the quantum effective action and the ground state wave function of a field theory. This method, along with a gauge-invariant mass term and the previously obtained vacuum wave function, is used to arrive at…
Recently, the {\it spacelike} part of the $SU(2)$ Yang--Mills equations has been identified with geometrical objects of a three--dimensional space of constant Riemann--Cartan curvature. We give a concise derivation of this Ashtekar type…
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…
A complexification of the twisted $\N=2$ theory allows one to determine the N=4 Yang--Mills theory in its third twist formulation. The imaginary part of the gauge symmetry is used to eliminate two scalars fields and create gauge covariant…
The deformed Hermitian Yang-Mills (dHYM) equation is a special Lagrangian type condition in complex geometry. It requires the complex analogue of the Lagrangian phase, defined for Chern connections on holomorphic line bundles using a…
We define a state space and a Markov process associated to the stochastic quantisation equation of Yang-Mills-Higgs (YMH) theories. The state space $\mathcal{S}$ is a nonlinear metric space of distributions, elements of which can be used as…
We propose that chiral two-dimensional Yang-Mills theory on a Riemann surface is dual to a deformed stationary subsector of the Gromov-Witten theory of that Riemann surface. Firstly, we argue that the algebraic structure that underlies the…
Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the…
Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled (1+1)-dimensional principal chiral sigma models. The $SU(N)\times SU(N)$ principal chiral sigma model in 1+1 dimensions is integrable, asymptotically free and has…
We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us…
U(n) Yang-Mills theory on the fuzzy sphere S^2_N is quantized using random matrix methods. The gauge theory is formulated as a matrix model for a single Hermitian matrix subject to a constraint, and a potential with two degenerate minima.…
A long-standing conjecture on the structure of renormalized, gauge invariant, integrated operators of arbitrary dimension in Yang-Mills theory is established. The general solution of the consistency condition for anomalies with sources…
In this article, we reconsider the formulation of Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory, and we investigate to what extent this symmetry lifts to the beta/gamma-deformation of the model. We first apply cohomology…
Quantum properties of topological Yang-Mills theory in (anti-)self-dual Landau gauge were recently investigated by the authors. We extend the analysis of renormalizability for two generalized classes of gauges; each of them depending on one…
We present a discretisation of the 3+1 formulation of the Yang-Mills equations in the temporal gauge, using a Lie algebra-valued extension of the discrete de Rham (DDR) sequence, that preserves the non-linear constraint exactly. In contrast…
Using the background field method, we study in a general covariant gauge the renormalization of the 6-dimensional Yang-Mills theory. This requires background gauge invariant counterterms, some of which do not vanish on shell. Such…