Non-perturbative Landau gauge and infrared critical exponents in QCD

We discuss Faddeev-Popov quantization at the non-perturbative level and show that Gribov's prescription of cutting off the functional integral at the Gribov horizon does not change the Schwinger-Dyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov's prescription is not exact, and we therefore turn to the method of stochastic quantization in its time-independent formulation, and recall the proof that it is correct at the non-perturbative level. The non-perturbative Landau gauge is derived as a limiting case, and it is found that it yields the Faddeev-Popov method in Landau gauge with a cut-off at the Gribov horizon, plus a novel term that corrects for over-counting of Gribov copies inside the Gribov horizon. Non-perturbative but truncated coupled Schwinger-Dyson equations for the gluon and ghost propagators $D(k)$ and $G(k)$ in Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by $D(k) \sim 1/(k^2)^{1 + a_D}$ and $G(k) \sim 1/(k^2)^{1 + a_G}$ are obtained in space-time dimensions $d = 2, 3, 4$. Two possible solutions are obtained with the values, in $d = 4$ dimensions, $a_G = 1, a_D = -2$, or $a_G = [93 - (1201)^{1/2}]/98 \approx 0.595353, a_D = - 2a_G$.Comment: 26 pages. Modified 2.25.02 to update references and to clarify Introduction and Conclusio

Manifest Duality in Born-Infeld Theory

Born-Infeld theory is formulated using an infinite set of gauge fields, along the lines of McClain, Wu and Yu. In this formulation electromagnetic duality is generated by a fully local functional. The resulting consistency problems are analyzed and the formulation is shown to be consistent.Comment: 15 pages, Late

Numerical Stochastic Perturbation Theory. Convergence and features of the stochastic process. Computations at fixed (Landau) Gauge

Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected fluctuations in the observables and give some idea to reduce them. In the end we show that also computation of quantities at fixed (Landau) Gauge is now possible.Comment: 3 pages. Contributed to 17th International Symposium on Lattice Field Theory (LATTICE 99), Pisa, Italy, 29 Jun - 3 Jul 199

SU(2) Landau gluon propagator on a 140^3 lattice

We present a numerical study of the gluon propagator in lattice Landau gauge for three-dimensional pure-SU(2) lattice gauge theory at couplings beta = 4.2, 5.0, 6.0 and for lattice volumes V = 40^3, 80^3, 140^3. In the limit of large V we observe a decreasing gluon propagator for momenta smaller than p_{dec} = 350^{+ 100}_{- 50} MeV. Data are well fitted by Gribov-like formulae and seem to indicate an infra-red critical exponent kappa slightly above 0.6, in agreement with recent analytic results.Comment: 5 pages with 2 figures and 3 tables; added a paragraph on discretization effect

Residual internal stress in partially crystallized photothermorefractive glass: Evaluation by nuclear magnetic resonance spectroscopy and first principles calculations

In some circumstances, the mechanical and optical properties of multiphase brittle materials strongly depend on the level of residual micromechanical stresses that arise upon cooling due to thermal and elastic mismatch between the constituent phases. Here we study the residual internal stress in a partially crystallized oxyfluoride glass, best known as photothermorefractive (PTR) glass. This material is composed of a glass matrix with embedded nanosize sodium fluoride (NaF) crystals. Using both the Selsing model and solid-state nuclear magnetic resonance in combination with first principles calculations we found that the crystals are under a tensile stress field of approximately 610-800 MPa. For this stress level the estimated critical crystal diameter for spontaneous cracking is about 2300-1900 nm, which greatly exceeds the observed diameters of 7-35 nm. Hence no spontaneous cracking is expected for the PTR glasses. First principles calculations indicate that the stress induced change of the refractive index of the NaF crystals is about -0.08%, which agrees with the observed refractive index changes

Charge density and electric charge in quantum electrodynamics

The convergence of integrals over charge densities is discussed in relation with the problem of electric charge and (non-local) charged states in Quantum Electrodynamics (QED). Delicate, but physically relevant, mathematical points like the domain dependence of local charges as quadratic forms and the time smearing needed for strong convergence of integrals of charge densities are analyzed. The results are applied to QED and the choice of time smearing is shown to be crucial for the removal of vacuum polarization effects responible for the time dependence of the charge (Swieca phenomenon). The possibility of constructing physical charged states in the Feynman-Gupta-Bleuler gauge as limits of local states vectors is discussed, compatibly with the vanishing of the Gauss charge on local states. A modification by a gauge term of the Dirac exponential factor which yields the physical Coulomb fields from the Feynman-Gupta-Bleuler fields is shown to remove the infrared divergence of scalar products of local and physical charged states, allowing for a construction of physical charged fields with well defined correlation functions with local fields

Equal-time two-point correlation functions in Coulomb gauge Yang-Mills theory

We apply a functional perturbative approach to the calculation of the equal-time two-point correlation functions and the potential between static color charges to one-loop order in Coulomb gauge Yang-Mills theory. The functional approach proceeds through a solution of the Schroedinger equation for the vacuum wave functional to order g^2 and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function, and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders.Comment: 33 pages, 7 figures with Feyman diagrams generated with pstricks; revised version with additional references and comments on possible applications added in the conclusions; accepted for publication in Nucl. Phys.

Inhomogeneous phase of a Gluon Plasma at finite temperature and density

By considering the non-perturbative effects associated with the fundamental modular region, a new phase of a Gluon Plasma at finite density is proposed. It corresponds to the transition from glueballs to non-perturbative gluons which condense at a non vanishing momentum. In this respect the proposed phase is analogous to the color superconducting LOFF phase for fermionic systems.Comment: 5 pages, 2 figure

Developments and new applications of numerical stochastic perturbation theory

A review of new developments in numerical stochastic perturbation theory (NSPT) is presented. In particular, the status of the extension of the method to gauge fixed lattice QCD is reviewed and a first application to compact (scalar) QED is presented. Lacking still a general proof of the convergence of the underlying stochastic processes, a self-consistent method for testing the results is discussed.Comment: 3 pages, 1 figure. Poster presented at the Lattice97 conference, Edinburgh, U

New issues for Numerical Stochastic Perturbation Theory

First attempts in the application of Numerical Stochastic Perturbation Theory (NSPT) to the problem of pushing one loop further the computation of SU(3) (SU(2)) pertubative beta function (in different schemes) are reviewed and the relevance of such a computation is discussed. Other issues include the proposal of a different strategy for gauge-fixed NSPT computations in lattice QCD.Comment: 3 pages, Latex, LATTICE98(algorithms