Related papers: The regularization and determination of the Yang-M…
We compute the Yang-Mills vacuum wave functional in three dimensions at weak coupling with O(e^2) precision. We use two different methods to solve the Schroedinger functional equation. One of them generalizes to O(e^2) the method followed…
We investigate Yang-Mills theory in 2+1 dimensions in the Schroedinger representation. The Schroedinger picture is interesting because it is well suited to explore properties of the vacuum state in the non-perturbative regime. Yet, not much…
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…
Working in a Hamiltonian formulation with $A_0 = 0$ gauge and also in a path integral formulation, we show that the vacuum wave functional of four-dimensional pure Yang-Mills theory has the form of the exponential of a {\it…
A method of measuring relative probabilities of various gauge-field configurations in the Yang-Mills vacuum was proposed long ago [Phys. Lett. B 223 (1989) 207]. We applied this method to compute the square of the YM vacuum wave functional…
We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in 2+1 dimensions…
In the first part of this paper, we present a set of simple arguments to show that the two-dimensional gauge anomaly and the (2+1)-dimensional Lorentz symmetry determine the leading Gaussian term in the vacuum wave function of…
Renormalization group transformations for Schr\"odinger equation are performed in $\phi^4$ and in Yang-Mills theories. The dependence of the ground state wave functional on rapidly oscillating fields is found. For Yang-Mills theory, this…
We proposed a simple Ansatz for the vacuum wave functional (VWF) of SU(2) gauge theory in temporal gauge. In 2+1 dimensions, the Ansatz was shown to be a fairly good approximation to the true VWF of the theory. Relative probabilities of…
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)…
We present an analytical continuum calculation, starting from first principles, of the vacuum wavefunction and string tension for pure Yang-Mills theories in $(2+1)$ dimensions, extending our previous analysis using gauge-invariant matrix…
We discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime. The approach is based on the use of local gauge invariant variables in the Schr\"odinger representation and the large $N$, planar…
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…
In this note we discuss the wave functional approach to the spectrum of pure Yang-Mills theory in 2+1 and 3+1 dimensions by highlighting the issues of dynamical mass generation and the role played by the kinetic term. We extrapolate our…
We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills Schrodinger equation in both the free-field limit, and in a strong-field zero mode limit.…
We explore the relationship between the quantum effective action and the ground state (and excited state) wave functions of a field theory. Applied to the Yang-Mills theory in 2+1 dimensions, we find the leading terms of the effective…
Three-dimensional Yang-Mills theory is investigated in the Hamiltonian formalism based on the Karabali-Nair variable. A new algorithm is developed to obtain the renormalized Hamiltonian by identifying local counterterms in Lagrangian with…
We present details of the analytic computation of the spectrum of lowest spin glueballs in pure Yang-Mills theory in 2+1 dimensions. The new ingredient is provided by the conjectured new non-trivial expression for the (quasi)Gaussian part…
We carry out further analysis of the Hamiltonian approach to Yang-Mills theory in 2+1 dimensions which helps to place the calculation of the vacuum wave function and the string tension in the context of a systematic expansion scheme. The…
For the special case of compact QED in (2+1) dimensions, we calculate the non-Gaussian vacuum wave-functional to second order in the monopole fugacity and obtain the effective photon mass. Our method presents some hope for understanding the…