P. Weisz

ANOMALIES OF THE FREE LOOP WAVE EQUATION IN THE WKB APPROXIMATION

We derive a well-defined, reparametrization invariant expression for the next to leading term in the small ħ expansion of the euclidean loop Green functional ψ(C). To this order in ħ, we then verify that ψ(C) satisfies a renormalized loop wave equation, which involves a number of local, but non-harmonic anomalous terms. Also, we find that the quantum fluctuations of the string give rise, in 3 + 1 dimensions, to a correction of the static quark potential by an attractive Coulomb potential of universal strength αstring = 112π.

Continuum limit improved lattice action for pure Yang-Mills theory (I)☆

Abstract Symanziks programme for constructing a lattice action with improved continuum limit behaviour is considered for the case of pure Yang-Mills theory. The structure of the action is proposed and discussed in detail to lowest order in perturbation theory.

Susskind Fermions on a Euclidean Lattice

A version of euclidean lattice QCD obtained by introducing the fermions using Susskinds method is described and certain properties discussed. A U(1) axial current having the correct axial anomaly in the continuum limit is identified. We find ΛminΛL,Suss = 28.78 for SU(3) with 4 flavors.

Scaling laws and triviality bounds in the lattice φ4 theory: (I). One-component model in the symmetric phase

Abstract The lattice φ 4 theory in four space-time dimensions is most likely “trivial”, i.e. its continuum limit is a free field theory. However, for small but positive lattice spacing a at energies well below the cutoff mass Λ = 1/ a , the theory effectively behaves like a continuum theory with particle interactions, which may be appreciable. By a combination of known analytical methods, we here determine the maximal value of the renormalized coupling at zero momentum as a function of Λ / m , where m denotes the mass of the scalar particle in the theory. Moreover, a complete solution of the model is obtained in the sense that all low energy amplitudes can be computed with reasonable estimated accuracy for arbitrarily chosen bare coupling and mass in the symmetric phase region.

How thick are chromo-electric flux tubes?

Abstract We analyse the space dependence of the expectation value of the chromo-electric energy density in the presence of a static quark-antiquark pair by means of the strong coupling expansion on a lattice and by the relativistic string model. Both methods indicate that the transversal width of the field energy distribution increases without bound, when the quark-antiquark separation goes to infinity.

Scaling laws and triviality bounds in the lattice φ4 theory: (II). One-component model in the phase with spontaneous symmetry breaking

Our earlier analysis of the lattice φ4 theory in four dimensions is extended to a neighborhood of the critical line in the broken symmetry phase, which includes the “scaling region” characterized by amR ⩽ 0.5 (a: lattice spacing, mR: renormalized particle mass). As in the symmetric phase, the renormalized coupling gR at zero momentum is bounded by a function of the cutoff Λ = 1/a, which decreases logarithmically as Λ → ∞. The maximal possible value of gR in the scaling region is found to be about 23 of the tree level unitary bound, i.e. the coupling is never really strong and bound state particles, if they exist at all, are expected to have a small binding energy. In terms of the renormalized vacuum expectation value νR of the field φ, the upper bound on the coupling corresponds to mR ⩽ 3.2νR.

Computation of the action for on-shell improved lattice gauge theories at weak coupling

Abstract The coefficient in Symanziks improved lattice action for (pure) SU(2) and SU(3) gauge theories are determined to one-loop order by requiring the absence of leading scaling violations in a set of on-shell quantities, which arise in a world where two dimensions are compactified in a twisted manner.

Efficient numerical techniques for perturbative lattice gauge theory computations

Abstract We discuss a set of methods and numerical tools, which are useful for a computer based approach to perturbative calculations in lattice gauge theory. The topics considered include the automatic generation of gluon vertex programs, a derivation of the Faddeev-Popov determinant on lattices with boundary, the use of a partially finite lattice with twisted boundary conditions as an infrared cutoff without zero modes, and finally the numerical extrapolation of lattice Feynman diagrams to the continuum limit. As an illustration of the methods we describe their implementation in the computation of the on-shell improved lattice action at weak coupling.

Monte Carlo Study of the Standard SU(2) Higgs Model

Abstract The SU(2) Higgs model with scalar doublet field is numerically investigated on lattices with size between 8 4 and 12 4 . Masses and zero momentum couplings are determined at several points of the three-dimensional coupling parameter space. Particular interest is given to questions related to the order of the confinement-Higgs phase transition. It is shown that for non-perturbative scalar self-couplings numerical Monte Carlo calculations are possible in the region of weak gauge coupling approximately equal to the physical value in the standard SU(2) ⊗ U(1) electroweak theory. Our first exploratory results in such a point on 12 4 lattice give a Higgs mass to W-mass ratio 6.4 ± 0.8 and a Higgs-WW coupling roughly a factor 3 smaller than the tree-level value. The circumstances under which these numbers could have some phenomenological relevance are discussed. A possible strategy is outlined for future large scale Monte Carlo calculations in the strongly self-interacting standard Higgs model with weak gauge coupling.

Numerical study of finite volume effects in the 4-dimensional Ising model

Abstract The effect of the finite lattice size on physical quantities, like masses and coupling constants, is numerically investigated in the 4-dimensional Ising model. The feasibility to obtain numerical information about low energy scattering from finite volume effects in a lattice Monte Carlo calculation is demonstrated.