Related papers: In quest of the Yang-Mills vacuum wavefunctional
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…
The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This…
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…
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)…
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…
For small values of the gauge coupling constant, we compare the densities of the energy of the vacuum and of the order parameter, evaluated in the lattice Monte Carlo simulation and in the perturbative field theory at two loop (Minkowski).…
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…
We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with…
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…
Toroidally compactified Yang-Mills theory on the lattice is studied by using the Hybrid Monte Carlo algorithm. When the compact dimensions are small, the theory naturally reduces to Yang-Mills with scalars. We confirm previous analytical…
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 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…
Numerical simulations of supersymmetric theories on the lattice are intricate and challenging with respect to their theoretical foundations and algorithmic realisation. Nevertheless, the simulations of a four-dimensional supersymmetric…
In this article we analyze the vacuum structure of pure SU(2) Yang-Mills using non-perturbative techniques. Monte Carlo simulations are performed for the lattice gauge theory with external sources to obtain the effective potential. Evidence…
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…
By generalizing our previous work on the parity symmetry, the partition function of a Yang-Mills theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated…
The derivation of the explicit formula for the vacuum expectation value of the Wilson loop functional for an arbitrary gauge group on an arbitrary orientable two-dimensional manifold is considered both in the continuum case and on the…
Recently Anishetty, Majumdar and Sharatchandra have proposed a way of characterizing topologically non-trivial configurations for 2+1-dimensional Yang-Mills theory in a local and manifestly gauge invariant manner. Here we develop criteria…
Supersymmetric Yang Mills theory is directly accessible to lattice simulations using current methodology, and can provide a non-trivial check of recent exact results in SQCD. In order to tune the lattice simulation to the supersymmetric…
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…