On the phenomenological theory of diffusion

A phenomenological theory of diffusion is given along the lines of the treatment of De Groot and Mazur¹). Simple relations between the diffusion matrices of the various kinds of composition variables are established. In linear approximation all kinds of composition variables obey Fick's second law. The special role of the mean volume velocity is discussed and attention is given to Onsager coefficients and mobilities (friction coefficients).     

On the triple-Pomeron vertex in perturbative QCD

We estimate the size of the triple-pomeron vertex in perturbative QCD and compare with the phenomenological value extracted from Regge fits to the experimental data. For simplicity, the results of the QCD analysis are taken in the large-N_c limit. We find that the perturbative triple-pomeron coupling is of the same order of magnitude as the observed one. We also estimate the size of the pomeron self-energy and its contribution to the renormalization of the pomeron intercept. The effect is very small, in agreement with previous non-perturbative estimates. Received: 9 October 2002 / Published online: 20 December 2002     

On the classification of simple vertex operator algebras

Inspired by a recent work of Frenkel-Zhu, we study a class of (pre-)vertex operator algebras (voa) associated to the self-dual Lie algebras. Based on a few elementary structural results we propose thatV, the category of Z₊-graded prevoasV in whichV[0] is one-dimensional, is a proper setting in which to study and classify simple objects. The categoryV is organized into what we call the minimalk ^th types. We introduce a functor —which we call the Frenkel-Lepowsky-Meurman functor—that attaches to each object inV a Lie algebra. This is a key idea which leads us to a (relative) classification of thesimple minimal first type. We then study the set of all Virasoro structures on a fixed minimal first typeV, and show that they are in turn classified by the orbits of the automorphism group Aut((V)) in cent((V)). Many new examples of voas are given. Finally, we introduce a generalized Kac-Casimir operator and give a simple proof of the irreducibility of the prolongation modules over the affine Lie algebras.     

On the Šilov boundary of the vertex function

The ilov boundary of the vertex function is computed without resource to analytic completion techniques.The research reported in this document has been supported in part by the Aerospace Research Laboratories under Grant No. AF EOAR 65–80, through the European Office of Aerospace Research (OAR), U.S. Air Force.This work is part of a thesis submitted to the Senate of the Technion-Israel Institute of Technology, as partial fulfilment of the requirements for a Ph.D. degree.     

On phenomenological models of lattice dynamics

The metallic interaction is split into (i) closed-shell part and (ii) ion- electron-ion part. The former is evaluated using non-central forces upto the third neighbour and the latter is obtained from the concept of bulk modulus of the electron gas. Phonon dispersion relations of h.c.p. scandium have been calculated and compared with the experimental results.     

On phenomenological electrodynamics of gyrotropic media

Using the principle of symmetry of the kinetic coefficients the material equation structure in gyrotropic media with sharp boundaries is determined. The obtained results are also valid in the presence of energy losses in the surface layer.     

On the dilaton vertex in the covariant formulation of strings

We investigate the dilaton vertex operator in the covariant formulation of strings. We find that the Faddeev-Popov ghosts play an essential role to construct conformal fields.     

On the solution of some vertex models using factorizableS matrices

The intimate connection between factorizableS matrices and some vertex models in two dimensions (to be reviewed here) is exploited to show that the knowledge of theS matrix not only allows us to define a solvable vertex modelá la Zamolodchikov, but often to write down the free energy by inspection. The prototype for discussion is Baxter's eight-vertex model generated by Zamolodchikov's Z₄ S matrix. The method is then applied to a hitherto unsolved 19-vertex model, based on the isospin-1S matrix of Zamolidchikov and Fateev, and agreement is checked to fourth order in a perturbation series. The possibility of molding other problems like theq-state Potts model into this framework is considered.Research supported in part by NSF grant No. INT 8117361.     

On the phenomenological rate equation in a model exchange reaction

The limits of validity of the phenomenological rate equation, and the phenomenological rate constant k_f and k_b are found for the exchange reaction $\text{A + BC}\textcolor{red}{}\text{AB + C}$ within the framework of simple multistate models. The possibility of macroscopically long transient times is discussed. The rate constants are shown to depend on the total densities n_A, n_B and n_C of the chemical species present in the mixture, when nonequilibrium effects are important. The distinction between a rate constant and a flux coefficient is illustrated. Differences among exchange, dissociation-recombination, and isomerization reactions in that regard are discussed.     

N-Superstring vertex and the vertex operator for the emission of the superstring

The BRST invariant, supersymmetric N-string vertex which applies to both, the Neveu-Schwarz and Ramond sector of the superstring is formulated using the vertex operator for the emission of a superstring. It is shown that the N-superstring vertex thus obtained is cyclic symmetric when GSO projected on-shell states and operators for the external strings are applied. The constraint equations of this vertex and their singularity structure are examined and we show that this vertex also has the required property of a transition operator. We also give a proof of its BRST invariance and supersymmetry.     

On the phenomenological description of surface absorption of light by metals

Fresnel’s formulas for the coefficients of light reflection from a metal surface are refined to take into account light absorption by conduction electrons during their reflection from the boundary of the metal. The estimates obtained show that the refinement may reveal itself in ellipsometric measurements if their errors do not exceed ∼0.5%.     

On the phenomenological group in the unified SO(10) model

We analyze possible low energy effects of the additional U(1) contained in the symmetry breaking chain: SO(10)→SU(5) ? U(1) →…, stressing the importance of considering extensions of SU(2) ? U(1) as subgroups of grand unified models, in order to use the relations between the coupling constants provided by the renormalization group. We also investigate the possibility of employing this extra U(1) for an explanation of the possible discrepancy between the experimental value of sin²θ_w and its renormalized value in the SU(5) model.     

On the phenomenological theory of the linear electrooptical effect in uniaxial crystals

The linear electrooptical effect in uniaxial crystals is considered with the aid of direct tensor methods. Covariant expressions for finding biradials and ray refractive indices are developed. A general expression is derived relating the nonlinear optical polarizability parameters and the electrooptical properties of a crystal. The results are applied to cuts of uniaxial ammonium dihydrogen phosphate (ADP), potassium dihydrogen phosphate (PDP), and quartz crystals often used for light modulation. The induced phase differences between the light waves propagating in such crystals are found for the field orientations considered.     

Measuring the triple-gluon vertex

The triple-gluon vertex can be measured from the gluon jet spread using the energy-cone distribution functions.     

On some three-meson vertex sum rules in quantum chromodynamics

We discuss some applications of the Laplace transform sum rules to the three-point function of currents and current divergences. Evaluating the QCD part of the vertex function in the symmetrical subtraction configuration, where all external masses are equal and much larger thanΛ _QCD, we obtain relations between the meson couplingsg _ωρπ,g _δKK ,g _ρππ and quark masses and vacuum condensates.     

On the phenomenological approach to dual resonance models for deep inelastic electroproduction

We outline a systematic procedure for constructing a dual resonance model for deep inelastic electroproduction which incorporates locality, current algebra, Regge behaviour, Bjorken scaling and the Dashen — Fubini — Gell-Mann sum rule. We illustrate the procedure in terms of a simple Ansatz for theW ₂ electroproduction structure function.     

On the colour contribution to effective weak vertex in broken colour gauge theories

Treating the breaking of colour symmetry via the mixing between the colour gluons and weak bosons (a la Rajasekaran and Roy) it is observed that the colour contribution to the effective weak vertex of a quark at zero momentum transfer is zero uptoO(α). An erratum to this article is available at .