The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge

The local composite operator A^2 is added to the Zwanziger action, which implements the restriction to the Gribov region in Euclidean Yang-Mills theories in the Landau gauge. We prove the renormalizability of this action to all orders of perturbation theory. This allows to study the dimension two gluon condensate by the local composite operator formalism when the restriction is taken into account. The effective action is evaluated at one-loop order in the MSbar scheme. We obtain explicit values for the Gribov parameter and for the mass parameter due to , but the expansion parameter turns out to be rather large. Furthermore, an optimization of the perturbative expansion in order to reduce the dependence on the renormalization scheme is performed. The properties of the vacuum energy, with or without , are investigated. It is shown that in the original Gribov-Zwanziger formulation (without ), the vacuum energy is always positive at 1-loop order, independently from the renormalization scheme and scale. With , we are unable to come to a definite conclusion at the order considered. In the MSbar scheme, we still find a positive vacuum energy, again with a relatively large expansion parameter, but there are renormalization schemes in which the vacuum energy is negative, albeit the dependence on the scheme itself appears to be strong. We recover the well known consequences of the restriction, and this in the presence of : an infrared suppression of the gluon propagator and an enhancement of the ghost propagator. This behaviour is in qualitative agreement with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations.Comment: 42 pages, 10 .eps figures. v2: Version accepted for publication in Phys.Rev.D. Added references. Technical details have been collected in two appendice

A time-dependent perturbative analysis for a quantum particle in a cloud chamber

We consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \in \mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.Comment: 23 page

Wide-field weak lensing by RXJ1347-1145

We present an analysis of weak lensing observations for RXJ1347-1145 over a 43' X 43' field taken in B and R filters on the Blanco 4m telescope at CTIO. RXJ1347-1145 is a massive cluster at redshift z=0.45. Using a population of galaxies with 20<R<26, we detect a weak lensing signal at the p<0.0005 level, finding best-fit parameters of \sigma_v=1400^{+130}_{-140} km s^{-1} for a singular isothermal sphere model and r_{200} = 3.5^{+0.8}_{-0.2} Mpc with c = 15^{+64}_{-10} for a NFW model in an \Omega_m = 0.3, \Omega_\Lambda = 0.7 cosmology. In addition, a mass to light ratio M/L_R =90 \pm 20 M_\odot / L_{R\odot} was determined. These values are consistent with the previous weak lensing study of RXJ1347--1145 by Fischer and Tyson, 1997, giving strong evidence that systemic bias was not introduced by the relatively small field of view in that study. Our best-fit parameter values are also consistent with recent X-ray studies by Allen et al, 2002 and Ettori et al, 2001, but are not consistent with recent optical velocity dispersion measurements by Cohen and Kneib, 2002.Comment: accepted to ApJ, tentative publication 10 May 2005, v624

Gauge-Invariant Coordinates on Gauge-Theory Orbit Space

A gauge-invariant field is found which describes physical configurations, i.e. gauge orbits, of non-Abelian gauge theories. This is accomplished with non-Abelian generalizations of the Poincare'-Hodge formula for one-forms. In a particular sense, the new field is dual to the gauge field. Using this field as a coordinate, the metric and intrinsic curvature are discussed for Yang-Mills orbit space for the (2+1)- and (3+1)-dimensional cases. The sectional, Ricci and scalar curvatures are all formally non-negative. An expression for the new field in terms of the Yang-Mills connection is found in 2+1 dimensions. The measure on Schroedinger wave functionals is found in both 2+1 and 3+1 dimensions; in the former case, it resembles Karabali, Kim and Nair's measure. We briefly discuss the form of the Hamiltonian in terms of the dual field and comment on how this is relevant to the mass gap for both the (2+1)- and (3+1)-dimensional cases.Comment: Typos corrected, more about the non-Abelian decomposition and inner products, more discussion of the mass gap in 3+1 dimensions. Now 23 page

Discovery of a Galaxy Cluster via Weak Lensing

We report the discovery of a cluster of galaxies via its weak gravitational lensing effect on background galaxies, the first spectroscopically confirmed cluster to be discovered through its gravitational effects rather than by its electromagnetic radiation. This fundamentally different selection mechanism promises to yield mass-selected, rather than baryon or photon-selected, samples of these important cosmological probes. We have confirmed this cluster with spectroscopic redshifts of fifteen members at z=0.276, with a velocity dispersion of 615 km/s. We use the tangential shear as a function of source photometric redshift to estimate the lens redshift independently and find z_l = 0.30 +- 0.08. The good agreement with the spectroscopy indicates that the redshift evolution of the mass function may be measurable from the imaging data alone in shear-selected surveys.Comment: revised version with minor changes, to appear in ApJ

Multiple Weak Deflections in Galaxy-Galaxy Lensing

The frequency and effects of multiple weak deflections in galaxy-galaxy lensing are investigated via Monte Carlo simulations. The lenses in the simulations are galaxies with known redshifts and known rest-frame blue luminosities. The frequency of multiple deflections above a given threshold shear value is quantified for discrete source redshifts, as well as for a set of sources that are broadly distributed in redshift space. In general, the closest lens in projection on the sky is not the only lens for a given source. In addition, ~50% of the time the closest lens is not the most important lens for a given source. Compared to a naive single-deflection calculation in which only the lensing due to the closest weak lens is considered, a full multiple-deflection calculation yields a higher net shear for individual sources, as well as a higher mean tangential shear around the lens centers. The full multiple-deflection calculation also shows that galaxy-galaxy lensing may contribute a substantial amount to cosmic shear on small angular scales. The degree to which galaxy-galaxy lensing contributes to the small-scale cosmic shear is, however, quite sensitive to the mass adopted for the halos of L_B* galaxies. Changing the halo mass by a factor of ~2.5 changes the contribution of galaxy-galaxy lensing to the cosmic shear by a factor of ~3 on scales of order 1 arcmin. The contribution of galaxy-galaxy lensing to cosmic shear decreases rapidly with angular scale and extrapolates to zero at scales of order 5 arcmin. This last result is roughly independent of the halo mass and suggests that for scales greater than about 5 arcmin, cosmic shear is insensitive to the details of the gravitational potentials of large galaxies.Comment: accepted for publication in ApJ; 35 pages, 15 figures; full text with high-resolution Figure 1 available at http://firedrake.bu.edu/preprints/preprints.htm

The Landau gauge gluon and ghost propagator in the refined Gribov-Zwanziger framework in 3 dimensions

In previous works, we have constructed a refined version of the Gribov-Zwanziger action in 4 dimensions, by taking into account a novel dynamical effect. In this paper, we explore the 3-dimensional case. Analogously as in 4 dimensions, we obtain a ghost propagator behaving like $1/p^2$ in the infrared, while the gluon propagator reaches a finite nonvanishing value at zero momentum. Simultaneously, a clear violation of positivity by the gluon propagator is also found. This behaviour of the propagators turns out be in agreement with the recent numerical simulations.Comment: 26 pages, 16 .eps figures. v3: version accepted for publication in Phys Rev

Extremality of Gaussian quantum states

We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key distillation and the classical capacity of Bosonic quantum channels. We prove that for every given covariance matrix the distillable secret key rate and the entanglement, if measured appropriately, are minimized by Gaussian states. This result leads to a clearer picture of the validity of frequently made Gaussian approximations. Moreover, it implies that Gaussian encodings are optimal for the transmission of classical information through Bosonic channels, if the capacity is additive.Comment: 4 page

More on Gribov copies and propagators in Landau-gauge Yang-Mills theory

Fixing a gauge in the non-perturbative domain of Yang-Mills theory is a non-trivial problem due to the presence of Gribov copies. In particular, there are different gauges in the non-perturbative regime which all correspond to the same definition of a gauge in the perturbative domain. Gauge-dependent correlation functions may differ in these gauges. Two such gauges are the minimal and absolute Landau gauge, both corresponding to the perturbative Landau gauge. These, and their numerical implementation, are described and presented in detail. Other choices will also be discussed. This investigation is performed, using numerical lattice gauge theory calculations, by comparing the propagators of gluons and ghosts for the minimal Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is found that the propagators are different in the far infrared and even at energy scales of the order of half a GeV. In particular, also the finite-volume effects are modified. This is observed in two and three dimensions. Some remarks on the four-dimensional case are provided as well.Comment: 23 pages, 16 figures, 6 tables; various changes throughout most of the paper; extended discussion on different possibilities to define the Landau gauge and connection to existing scenarios; in v3: Minor changes, error in eq. (3) & (4) corrected, version to appear in PR

On the exit statistics theorem of many particle quantum scattering

We review the foundations of the scattering formalism for one particle potential scattering and discuss the generalization to the simplest case of many non interacting particles. We point out that the "straight path motion" of the particles, which is achieved in the scattering regime, is at the heart of the crossing statistics of surfaces, which should be thought of as detector surfaces. We sketch a proof of the relevant version of the many particle flux across surfaces theorem and discuss what needs to be proven for the foundations of scattering theory in this context.Comment: 15 pages, 4 figures; to appear in the proceedings of the conference "Multiscale methods in Quantum Mechanics", Accademia dei Lincei, Rome, December 16-20, 200