Planckian Energy Scattering and Surface Terms in the Gravitational Action

This is a revised version of our previous paper by the same name and preprint number. It contains various changes, two figures and new results in sect.5. We propose a new approach to four-dimensional Planckian-energy scattering in which the phase of the ${\cal S}$-matrix is written---to leading order in $\hbar$ and to all orders in $R/b =Gs/J$---in terms of the surface term of the gravity action and of a boundary term for the colliding quanta. The proposal is checked at the leading order in $R/b$ and also against some known examples of scattering in strong gravitational fields.Comment: preprint CERN-TH.6904/93/rev (Latex file, 46 pages, 2 figures not included

Electromagnetic fields of a massless particle and the eikonal

Electromagnetic fields of a massless charged particle are described by a gauge potential that is almost everywhere pure gauge. Solution of quantum mechanical wave equations in the presence of such fields is therefore immediate and leads to a new derivation of the quantum electrodynamical eikonal approximation. The elctromagnetic action in the eikonal limit is localised on a contour in a two-dimensional Minkowski subspace of four-dimensional space-time. The exact S-matrix of this reduced theory coincides with the eikonal approximation, and represents the generalisatin to electrodynamics of the approach of 't Hooft and the Verlinde's to Planckian scattering.Comment: The missing overdot -- signifying the $\tau$ differentiation $\nabla^2 {\dot \Omega}^{+ -} and {\dot k}^{+-}$ in eqs. (23) and (24) -- is inserted. Also, obsolete macro has been fixed. Plain TeX, 13 page

Intermittency and structure functions in channel flow turbulence

We present a study of intermittency in a turbulent channel flow. Scaling exponents of longitudinal streamwise structure functions, $\zeta_p /\zeta_3$, are used as quantitative indicators of intermittency. We find that, near the center of the channel the values of $\zeta_p /\zeta_3$ up to $p=7$ are consistent with the assumption of homogeneous/isotropic turbulence. Moving towards the boundaries, we observe a growth of intermittency which appears to be related to an intensified presence of ordered vortical structures. In fact, the behaviour along the normal-to-wall direction of suitably normalized scaling exponents shows a remarkable correlation with the local strength of the Reynolds stress and with the \rms value of helicity density fluctuations. We argue that the clear transition in the nature of intermittency appearing in the region close to the wall, is related to a new length scale which becomes the relevant one for scaling in high shear flows.Comment: 4 pages, 6 eps figure

Intermittency and scaling laws for wall bounded turbulence

Well defined scaling laws clearly appear in wall bounded turbulence, even very close to the wall, where a distinct violation of the refined Kolmogorov similarity hypothesis (RKSH) occurs together with the simultaneous persistence of scaling laws. A new form of RKSH for the wall region is here proposed in terms of the structure functions of order two which, in physical terms, confirms the prevailing role of the momentum transfer towards the wall in the near wall dynamics.Comment: 10 pages, 5 figure

The Amati relation in the "fireshell" model

(Shortened) CONTEXT: [...] AIMS: Motivated by the relation proposed by Amati and collaborators, we look within the ``fireshell'' model for a relation between the peak energy E_p of the \nu F_\nu total time-integrated spectrum of the afterglow and the total energy of the afterglow E_{aft}, which in our model encompasses and extends the prompt emission. METODS: [...] Within the fireshell model [...] We can then build two sets of ``gedanken'' GRBs varying the total energy of the electron-positron plasma E^{e^\pm}_{tot} and keeping the same baryon loading B of GRB050315. The first set assumes for the effective CBM density the one obtained in the fit of GRB050315. The second set assumes instead a constant CBM density equal to the average value of the GRB050315 prompt phase. RESULTS: For the first set of ``gedanken'' GRBs we find a relation E_p\propto (E_{aft})^a, with a = 0.45 \pm 0.01, whose slope strictly agrees with the Amati one. Such a relation, in the limit B \to 10^{-2}, coincides with the Amati one. Instead, in the second set of ``gedanken'' GRBs no correlation is found. CONCLUSIONS: Our analysis excludes the Proper-GRB (P-GRB) from the prompt emission, extends all the way to the latest afterglow phases and is independent on the assumed cosmological model, since all ``gedanken'' GRBs are at the same redshift. The Amati relation, on the other hand, includes also the P-GRB, focuses on the prompt emission only, and is therefore influenced by the instrumental threshold which fixes the end of the prompt emission, and depends on the assumed cosmology. This may well explain the intrinsic scatter observed in the Amati relation.Comment: 4 pages, 5 figures, to appear on A&A Letter

Effective Action for High-Energy Scattering in Gravity

The multi-Regge effective action is derived directly from the linearized gravity action. After excluding the redundant field components we separate the fields into momentum modes and integrate over modes which correspond neither to the kinematics of scattering nor to the one of exchanged particles. The effective vertices of scattering and of particle production are obtained as sums of the contributions from the triple and quartic interaction terms and the fields in the effective action are defined in terms of the two physical components of the metric fluctuation.Comment: 15 pages, LATE

One particle cross section in the target fragmentation region: an explicit calculation in (\phi^3)_6

One particle inclusive cross sections in the target fragmentation region are considered and an explicit calculation is performed in (\phi^3)_6 model field theory. The collinear divergences can be correctly absorbed into a parton density and a fragmentation function but the renormalized cross section gets a large logarithmic correction as expected in a two scale regime. We find that the coefficient of such a correction is precisely the scalar DGLAP kernel. Furthermore the consistency of this result with an extended factorization hypothesis is investigated.Comment: latex, 16 pages including 8 postscript figure

On the Zero-Slope Limit of the Compactified Closed Bosonic String

In the framework of the compactified closed bosonic string theory with the extra spatial coordinates being circular with radius $R$, we perform both the zero-slope limit and the $R \rightarrow 0$ limit of the tree scattering amplitude of four massless scalar particles. We explicitly show that this double limit leads to amplitudes involving scalars which interact through the exchange of a scalar, spin 1 and spin 2 particle. In particular, this latter case reproduces the same result obtained in linearized quantum gravity.Comment: 10 pages, LaTex file, DSF-T-43/9