Instability of coherent states of a real scalar field

We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic nonlinearity. The linear analysis of time-dependent parts of perturbations leads to the Hill equation with a singular coefficient. To evaluate the characteristic exponent we extend the Lindemann-Stieltjes method, usually applied to the Mathieu and Lame equations, to the case that the periodic coefficient in the general Hill equation is an unbounded function of time. As a result, we derive the formula for the characteristic exponent and calculate the stability-instability chart. Then we analyze the spatial structure of the perturbations. Using these results we show that the pulsons of any amplitudes, remaining well-localized objects, lose their coherence with time. This means that, strictly speaking, all pulsons of the model considered are unstable. Nevertheless, for the nodeless pulsons the rate of the coherence breaking in narrow ranges of amplitudes is found to be very small, so that such pulsons can be long-lived. Further, we use the obtaned stability-instability chart to examine the Affleck-Dine type condensate. We conclude the oscillating condensate can decay into an ensemble of the nodeless pulsons.Comment: 11 pages, 8 figures, submitted to Physical Review

Abelian monopoles in finite temperature lattice SU(2) gluodynamics: first study with improved action

The properties of the thermal Abelian color-magnetic monopoles in the maximally Abelian gauge are studied in the deconfinement phase of the lattice SU(2) gluodynamics. To check universality of the monopole properties we employ the tadpole improved Symanzik action. The simulated annealing algorithm combined with multiple gauge copies is applied for fixing the maximally Abelian gauge to avoid effects of Gribov copies. We compute the density, interaction parameters, thermal mass and chemical potential of the thermal Abelian monopoles in the temperature range between Tc and 3Tc. In comparison with earlier findings our results for these quantities are improved either with respect to effects of Gribov copies or with respect to lattice artifacts.Comment: 11 pages, 14 figures, 5 tables; substantially changed version, title change

Positivity issues for the pinch-technique gluon propagator and their resolution

Although gauge-boson propagators in asymptotically-free gauge theories satisfy a dispersion relation, they do not satisfy the K\"allen-Lehmann (KL) representation because the spectral function changes sign. We argue that this is a simple consequence of asymptotic freedom. On the basis of the QED-like Ward identities of the pinch technique (PT) we claim that the product of the coupling $g^2$ and the scalar part $\hat{d}(q^2)$ of the PT propagator, which is both gauge invariant and renormalization-group invariant, can be factored into the product of the running charge $\bar{g}^2(q^2)$ and a term $\hat{H}(q^2)$ both of which satisfy the KL representation although their product does not. We show that this behavior is consistent with some simple analytic models that mimic the gauge-invariant PT Schwinger-Dyson equations (SDE) provided that the dynamic gauge boson mass is sufficiently large. The PT SDEs do not depend directly on the PT propagator through $\hat{D}$ but only through $\hat{H}$.Comment: 13 pages, revtex4. Same physics, shortened; version accepted for publication in Phys. Rev.

Infrared behavior and Gribov ambiguity in SU(2) lattice gauge theory

For SU(2) lattice gauge theory we study numerically the infrared behavior of the Landau gauge ghost and gluon propagators with the special accent on the Gribov copy dependence. Applying a very efficient gauge fixing procedure and generating up to 80 gauge copies we find that the Gribov copy effect for both propagators is essential in the infrared. In particular, our best copy dressing function of the ghost propagator approaches a plateau in the infrared, while for the random first copy it still grows. Our best copy zero-momentum gluon propagator shows a tendency to decrease with growing lattice size which excludes singular solutions. Our results look compatible with the so-called decoupling solution with a non-singular gluon propagator. However, we do not yet consider the Gribov copy problem to be finally resolved.Comment: 9 pages, 9 figure

Off-shell two loop QCD vertices

We calculate the triple gluon, ghost-gluon and quark-gluon vertex functions at two loops in the MSbar scheme in the chiral limit for an arbitrary linear covariant gauge when the external legs are all off-shell.Comment: 29 latex pages, 32 figures, anc directory contains txt file with electronic version of vertex functions for each of the three 3-point cases in the MSbar scheme and includes the projection matrice

Pseudo-Stable Bubbles

The evolution of spherically symmetric unstable scalar field configurations (``bubbles'') is examined for both symmetric (SDWP) and asymmetric (ADWP) double-well potentials. Bubbles with initial static energies E_0\la E_{{\rm crit}}, where $E_{{\rm crit}}$ is some critical value, shrink in a time scale determined by their linear dimension, or ``radius''. Bubbles with E_0\ga E_{{\rm crit}} evolve into time-dependent, localized configurations which are {\it very} long-lived compared to characteristic time-scales in the models examined. The stability of these configurations is investigated and possible applications are briefly discussed.tic time-scales in the models examined. The stability of these configurations is investigated and possible applications are briefly discussed.Comment: 10 pages, LaTeX (uses revtex 3.0), 4 figures (postscript files of figs.1 and 2 appended starting on line 497), report DART-HEP-93/0

Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate ⟨A2⟩\braket{A^2} in the Landau gauge

We consider the gluon propagator $D(p^2)$ at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate the tree level analytical prediction in terms of the (Refined) Gribov-Zwanziger framework. It turns out that an important role is played by the presence of the widely studied dimension two gluon condensate $\braket{A^2}$. Including this effect allows to obtain an acceptable fit up to 1 \'{a} 1.5 GeV, while corroborating the Refined Gribov-Zwanziger prediction for the gluon propagator. We also discuss the infinite volume extrapolation, leading to the estimate $D(0)=8.3\pm0.5\text{GeV}^{-2}$. As a byproduct, we can also provide the prediction $\braket{g^2 A^2}\approx 3\text{GeV}^2$ obtained at the renormalization scale $\mu=10\text{GeV}$.Comment: 17 pages, 10 figures, updated version, accepted for publication in Phs.Rev.

The gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: taking into account the effects of the Gribov copies and of the dimension two condensates

The infrared behavior of the gluon and ghost propagators is studied in SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge within the Gribov-Zwanziger framework. The nonperturbative effects associated with the Gribov copies and with the dimension two condensates are simultaneously encoded into a local and renormalizable Lagrangian. The resulting behavior turns out to be in good agreement with the lattice data.Comment: final version, to appear in Physical Review

Low momentum propagators at two loops in gluon mass model

We compute the two loop corrections to the gluon propagator for low momentum in a gluon mass model. This model has recently been proposed as an alternative to the Gribov construction in the way it handles Gribov copies in the gauge fixing. The corrections provide improvements for estimating the point where the gluon propagator freezes in relation to lattice data.Comment: 16 latex pages, 1 figur

Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function

We study the gluon propagator $D_{\mu\nu}^{ab}(x)$ in the Landau gauge in SU(3) lattice QCD at $\beta$ = 5.7, 5.8, and 6.0 at the quenched level. The effective gluon mass is estimated as $400 \sim 600$MeV for $r \equiv (x_\alpha x_\alpha)^{1/2} = 0.5 \sim 1.0$ fm. Through the functional-form analysis of $D_{\mu\nu}^{ab}(x)$ obtained in lattice QCD, we find that the Landau-gauge gluon propagator $D_{\mu\mu}^{aa}(r)$ is well described by the Yukawa-type function $e^{-mr}/r$ with $m \simeq 600$MeV for $r = 0.1 \sim 1.0$ fm in the four-dimensional Euclidean space-time. In the momentum space, the gluon propagator $\tilde D_{\mu\mu}^{aa}(p^2)$ with $(p^2)^{1/2}= 0.5 \sim 3$ GeV is found to be well approximated with a new-type propagator of $(p^2+m^2)^{-3/2}$, which corresponds to the four-dimensional Yukawa-type propagator. Associated with the Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff}(t)$, and the spectral function $\rho(\omega)$ of the gluon field. The mass parameter $m$ turns out to be the effective gluon mass in the infrared region of $\sim$ 1fm. As a remarkable fact, the obtained gluon spectral function $\rho(\omega)$ is almost negative-definite for $\omega >m$, except for a positive $\delta$-functional peak at $\omega=m$.Comment: 20 pages, 15 figure