Causal construction of the massless vertex diagram

The massless one-loop vertex diagram is constructed by exploiting the causal structure of the diagram in configuration space, which can be translated directly into dispersive relations in momentum space.Comment: 14 pages, LATEX with style file, corresponds to published versio

Local and Global relations between the number of contacts and density in monodisperse sphere packs

The topological structure resulting from the network of contacts between grains (\emph{contact network}) is studied for large samples of monosized spheres with densities (fraction of volume occupied by the spheres) ranging from 0.59 to 0.64. We retrieve the coordinates of each bead in the pack and we calculate the average coordination number by using three different methods. We show that, in the range of density investigated, the coordination number is larger than 4 and it increases with the packing fraction. At local level we also observe a positive correlation between local packing fraction and number of neighbors. We discover a dependence between the local densities of configurations with few neighbors in contact and the global sample-denities. This might indicate that local configurations with small number of neighbors are able to deform plastically when the sample is compactifying. PACS: 45.70.-n, Granular Systems; 45.70.Cc, Static sandpiles; Granular Compaction.Comment: 10 pages, 6 figure

Resummation of mass terms in perturbative massless quantum field theory

The neutral massless scalar quantum field $\Phi$ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form $-\frac{m^2}{2} \Phi^2$ to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.Comment: 15 pages, LaTeX (style files included), one section adde

Regularization in quantum field theory from the causal point of view

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.Comment: 75 pages, 8 figures, style file included, some comments and references adde

Focusing of high-energy particles in the electrostatic field of a homogeneously charged sphere and the effective momentum approximation

The impact of the strongly attractive electromagnetic field of heavy nuclei on electrons in quasi-elastic (e,e') scattering is often accounted for by the effective momentum approximation. This method is a plane wave Born approximation which takes the twofold effect of the attractive nucleus on initial and final state electrons into account, namely the modification of the electron momentum in the vicinity of the nucleus, and the focusing of electrons towards the nuclear region leading to an enhancement of the corresponding wave function amplitudes. The focusing effect due to the attractive Coulomb field of a homogeneously charged sphere on a classical ensemble of charged particles incident on the field is calculated in the highly relativistic limit and compared to results obtained from exact solutions of the Dirac equation. The result is relevant for the theoretical foundation of the effective momentum approximation and describes the high energy behavior of the amplitude of continuum Dirac waves in the potential of a homogeneously charged sphere. Our findings indicate that the effective momentum approximation is a useful approximation for the calculation of Coulomb corrections in (e,e') scattering off heavy nuclei for sufficiently high electron energies and momentum transfer.Comment: 16 pages, 9 figures, LATEX, some references adde

Holographic entropy bound from gravitational Fock space truncation

A simplified derivation of Yurtsever's result, which states that the entropy of a truncated bosonic Fock space is given by a holographic bound when the energy of the Fock states is constrained gravitationally, is given for asymptotically flat spacetimes with arbitrary dimension d greater or equal to four. For this purpose, a scalar field confined to a spherical volume in d-dimensional spacetime is considered. Imposing an upper bound on the total energy of the corresponding Fock states which ensures that the system is in a stable configuration against gravitational collapse and imposing a cutoff on the maximum energy of the field modes of the order of the Planck energy leads to an entropy bound of holographic type. A simple derivation of the entropy bound is also given for the fermionic case.Comment: 5 pages, Latex (incl. style file), minor typos correcte

Entropy Bound with Generalized Uncertainty Principle in General Dimensions

In this letter, the entropy bound for local quantum field theories (LQFT) is studies in a class of models of the generalized uncertainty principle(GUP) which predicts a minimal length as a reflection of the quantum gravity effects. Both bosonic and fermionic fields confined in arbitrary spatial dimension $d\geq4$ ball ${\cal B}^{d}$ are investigated. It is found that the GUP leads to the same scaling $A_{d-2}^{(d-3)/(d-2)}$ correction to the entropy bound for bosons and fermions, although the coefficients of this correction are different for each case. Based on our calculation, we conclude that the GUP effects can become manifest at the short distance scale. Some further implications and speculations of our results are also discussed.Comment: 8 pages, topos corrected and references adde

Coulomb Corrections for Coherent Electroproduction of Vector Mesons: Eikonal Approximation

Virtual radiative corrections due to the long range Coulomb forces of heavy nuclei with charge Z may lead to sizeable corrections to the Born cross section usually used for lepton-nucleus scattering processes. An introduction and presentation of the most important issues of the eikonal approximation is given. We present calculations for forward electroproduction production of rho mesons in a framework suggested by the VDM (vector dominance model), using the eikonal approximation. It turns out that Coulomb corrections may become relatively large. Some minor errors in the literature are corrected.Comment: 14 pages, 6 figures, published versio

Structural and entropic insights into the nature of the random-close-packing limit

Disordered packings of equal sized spheres cannot be generated above the limiting density (fraction of volume occupied by the spheres) of ??0.64 without introducing some partial crystallization. The nature of this “random-close-packing” limit (RCP) is investigated by using both geometrical and statistical mechanics tools applied to a large set of experiments and numerical simulations of equal-sized sphere packings. The study of the Delaunay simplexes decomposition reveals that the fraction of “quasiperfect tetrahedra” grows with the density up to a saturation fraction of ?30% reached at the RCP limit. At this limit the fraction of aggregate “polytetrahedral” structures (made of quasiperfect tetrahedra which share a common triangular face) reaches it maximal extension involving all the spheres. Above the RCP limit the polytetrahedral structure gets rapidly disassembled. The entropy of the disordered packings, calculated from the study of the local volume fluctuations, decreases uniformly and vanishes at the (extrapolated) limit ?K?0.66. Before such limit, and precisely in the range of densities between 0.646 and 0.66, a phase separated mixture of disordered and crystalline phases is observed