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Yang-Mills theory in four dimensions formally admits an exact Chern-Simons wavefunction. It is an eigenfunction of the quantum Hamiltonian with zero energy. It is known to be unphysical for a variety of reasons, but it is still interesting…
A gauge-invariant wavefunctional is proposed as an approximation to the ground state of Yang-Mills theory in 2+1 dimensions, quantized in temporal gauge. The proposed vacuum state is the true ground state of the appropriate Hamiltonian in…
A new set of gauge invariant variables is defined to describe the physical Hilbert space of $d = 3 + 1$ $SU(2)$ Yang-Mills theory in the fixed-time canonical formalism. A natural geometric interpretation arises due to the $GL(3)$ covariance…
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 consider the ordinary and noncommutative Dirac-Born-Infeld theories within the open string sigma-model. First, we propose a renormalization scheme, hybrid point splitting regularization, that leads directly to the Seiberg-Witten…
We examine an extension of the ideas of quantum cosmology and, in particular, the proposal of Hartle and Hawking for the boundary conditions of the Universe, to models which incorporate Yang-Mills fields. Inhomogeneous perturbations about a…
Inspired by the center-vortex dominance in the infrared sector of $SU(N)$ Yang-Mills theory observed on the lattice, we propose a vacuum wave functional localized on an ensemble of correlated center vortices endowed with stiffness and…
In this review we consider the Hamiltonian analysis of Yang-Mills theory and some variants of it in three spacetime dimensions using the Schr\"odinger representation. This representation, although technically more involved than the usual…
We suggest a means of obtaining certain Green's functions in 3+1-dimensional ${\cal N} = 4$ supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. The non-critical string theory is related to critical…
It is proposed an integral formulation of classical Yang-Mills equations in the presence of sources, based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections. The formulation leads…
The method of reduction of a non-Abelian gauge theory to the corresponding unconstrained system is exemplified for SU(2) Yang-Mills field theory. The reduced Hamiltonian which describes the dynamics of the gauge invariant variables is…
We quantize non-commutative Maxwell theory canonically in the background field gauge for weak and slowly varying background fields. We determine the complete basis for expansion under such an approximation. As an application, we derive the…
A globally converging numerical method to solve coupled sets of non-linear integral equations is presented. Such systems occur e.g. in the study of Dyson-Schwinger equations of Yang-Mills theory and QCD. The method is based on the knowledge…
The first paper attempting direct calculation of the Yang-Mills vacuum wave functional was published by Greensite in 1979. I review some recent results of the determination of the vacuum wave functional in Monte Carlo simulations of SU(2)…
The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass…
We investigated the SU(2) Einstein-Yang-Mills system on a time-dependent non-diagonal cylindrical symmetric space-time. From the numerical investigation, wave-like solutions are found, consistent with the familiar string-like features. They…
Most nonabelian gauge theories admit the existence of conserved and quantized topological charges as generalizations of the Dirac monopole. Their interactions are dictated by topology. In this paper, previous work in deriving classical…
We present the derivation of the Yang-Mills gauge theory based on the covariant Hamiltonian representation of Noether's theorem. As the starting point, we re-formulate our previous presentation of the canonical Hamiltonian derivation of…
Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite $N$ corrections in holography. We describe how the…
A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach…