Quark-hadron duality in electron-pion scattering

We explore the relationship between exclusive and inclusive electromagnetic scattering from the pion, focusing on the transition region at intermediate Q². Combining Drell-Yan data on the leading twist quark distribution in the pion with a model for the resonance region at large x, we calculate QCD moments of the pion structure function over a range of Q², and quantify the role of higher twist corrections. Using a parameterization of the pion elastic form factor and phenomenological models for the π↦ρ transition form factor, we further test the extent to which local duality may be valid for the pion. Received: 10 February 2003 / Accepted: 12 March 2003 / Published online: 27 May 2003     

Quasiclassical formalism and the Andreev equation

In this article I shall make explicit the connection between the quasiclassical Green’s function and the Andreev quasiparticle energies and wavefunctions. The physical meaning of the components of the Green’s function is elucidated.     

Spin-rotation formalism for Meson-Baryon scattering

A spin-rotation formalism is developed for the extraction of physical quantities from the reaction π^- p↑→K°Λ, using the Λ-decay as polarisation analyser. The method described here uses the parameters polarisation,P, and spin-rotation angle, β. Effects due to apparatus acceptance are explicitly included. The method has advantages in minimising the sensitivity to various systematic errors.     

Recursion relations and scattering amplitudes in the light-front formalism

The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off-shell scattering amplitudes which are light-front analogs of the Berends–Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on-shell we recover the scattering amplitudes previously derived in the literature.     

Quantum mechanics in the K-field formalism: Field equation

The paper considers a field equation for representing a microparticle as an extended object constructed from that field (K field). It is shown that in contrast to the equation of an S field (i.e., Schrödinger equation), the boundary-value problem for the K-field equation cannot be used for a unique determination of the parameters of a microparticle in steady states. An auxiliary equation, therefore, is necessary to ensure that the solution of the K -field equation is unique. This is in complete agreement with the physical meaning of K field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 30–33, August, 1995.     

Quark-hadron duality and meson-meson scattering amplitudes

We investigate a special concept of quarkhadron duality in meson physics at low and intermediate energies. With a relativistic propagator for confined quarks, we calculated masses and widths of the mesons which areS- andP-wave states ofq¯q (J ^P=0^?, 1^?, 0⁺, 1^+c, 2⁺) as well as meson-meson scattering amplitudes at energies up totrs ≤ 1.3 GeV by including light pseudoscalar and vector mesons into the interaction dynamics. Our investigation shows that the influence of the light meson dynamics resutls in:

1. a contribution to the constituent quark mass of approximately 200 MeV.
2. the appearance of a new soft confinement force barrier responsible for the formation of the highly excited meson states.

     

Stokes-space formalism for Bragg scattering in a fiber

Optical frequency conversion by four-wave mixing (Bragg scattering) in a fiber is considered. The evolution of this process can be modeled using the signal and idler amplitudes, which are complex, or Stokes-like parameters, which are real. The Stokes-space formalism allows one to visualize power and phase information simultaneously, and produces a simple evolution equation for the Stokes parameters.     

The continuity equation and the Hamiltonian formalism in quantum mechanics

The relationship between the continuity equation and the HamiltonianH of a quantum system is investigated from a nonstandard point of view. In contrast to the usual approaches, the expression of the current densityJ is givenab initio by means of a transport-velocity operatorV _T, whose existence follows from a weak formulation of the correspondence principle. Once given a Hilbert-space metricM, it is shown that the equation of motion and the continuity equation actually represent a system in theunknown operatorsH andV _T, due to the arbitrariness on the initial condition of the quantum state. The general solution is given in some cases of special interest and a straightforward application to relativistic quantum mechanics is performed.This work was partially supported by the Ministero della Pubblica Istruzione.     

The neutron-deuteron scattering problem in the framework of the Faddeev formalism

The three-body Faddeev equations in the configuration space are solved numerically for study of the neutron-deuteron scattering process above the breakup threshold. The amplitudes for the binary scattering process and breakup are obtained by the developed asymptotic approach.     

A study of duality of the ππ scattering amplitude

Dual structure of the ππ scattering amplitude has been investigated in terms of the finite energy sum rule using recent phase-shift data. The amplitude shows properties quite consistent with the simple dual model in the framework of the two component theory of duality.     

Test of duality in baryon-antibaryon amplitudes from Reggeon-particle scattering

By studying the backward production data for meson resonances we investigate the dual properties of baryon-Reggeised antibaryon elastic scattering. We find strong support for the duality prediction that meson resonances in the baryon antibaryon channel should be dual to an exotic trajectory.     

A new nonlinear-wave-equation formalism for stimulated Brillioun scattering

A revised formalism of SBS is given based on a new optical nonlinear wave equation which explicitly accounts for the macroscopic spatial inhomogeneity resulting from the induced acoustic wave in the medium. The new equation applies to other scattering phenomena, and more generally to optical wave propagation and interaction in nanostructured media for which characteristic spatial scale lengths of material structures (existing or optically induced) are smaller than the optical wavelength.     

Haag-Ruelle-Hepp scattering formalism for essentially local non-localizable fields

We generalize the axiom of locality to the non-localizable case by an axiom of essential locality which means a natural local continuity property of the field commutator on the light-cone. For localizable fields essential locality coincides with ordinary locality while localizable local fields restricted to non-localizable test spaces still remain essentially local. Essential locality is proved to be sufficient for a derivation of the usual Haag-Ruelle-Hepp scattering formalism. Functions of the free field are examples of essentially local fields which may not be localizable.     

Dispersion relation formalism for virtual Compton scattering off the proton

We present in detail a dispersion relation formalism for virtual Compton scattering (VCS) off the proton from threshold into the Δ(1232)-resonance region. Such a formalism can be used as a tool to extract the generalized polarizabilities of the proton from both unpolarized and polarized VCS observables over a larger energy range. We present calculations for existing and forthcoming VCS experiments and demonstrate that the VCS observables in the energy region between pion production threshold and the Δ(1232)-resonance show an enhanced sensitivity to the generalized polarizabilities. Received: 14 March 2001 / Accepted: 18 June 2001     

Two-photon exchange contributions to elastic ep scattering in the non-local field formalism

We construct a non-local gauge-invariant Lagrangian to model the electromagnetic interaction of the proton. The Lagrangian includes all allowed operators with dimension up to five. We compute the two-photon exchange contribution to elastic electron–proton scattering using this effective non-local Lagrangian. The one-loop calculation in this model includes the standard box and cross box diagram with the standard on-shell form of the hadron electromagnetic vertices. Besides this we find an extra contribution, which depends on an unknown constant. We use experimentally extracted form factors for our calculation. We find that the correction to the reduced cross section is slightly non-linear as a function of the photon longitudinal polarization ε. The non-linearity seen is within the experimental error bars of the Rosenbluth data. The final result completely explains the difference between the form factor ratio G_E/G_M extracted by Rosenbluth separation technique at SLAC and polarization transfer technique at JLAB.     

Boundary symmetries in linear differential and integral equation problems applied to the self-consistent Green’s function formalism of acoustic and electromagnetic scattering

Explicit symmetry relations for the Green’s function subject to homogeneous boundary conditions are derived for arbitrary linear differential or integral equation problems in which the boundary surface has a set of symmetry elements. For corresponding homogeneous problems subject to inhomogeneous boundary conditions implicit symmetry relations involving the Green’s function are obtained. The usefulness of these symmetry relations is illustrated by means of a recently developed self-consistent Green’s function formalism of electromagnetic and acoustic scattering problems applied to the exterior scattering problem. One obtains explicit symmetry relations for the volume Green’s function, the surface Green’s function, and the interaction operator, and the respective symmetry relations are shown to be equivalent. This allows us to treat boundary symmetries of volume-integral equation methods, boundary-integral equation methods, and the T matrix formulation of acoustic and electromagnetic scattering under a common theoretical framework. By specifying a specific expansion basis the coordinate-free symmetry relations of, e.g., the surface Green’s function can be brought into the form of explicit symmetry relations of its expansion coefficient matrix. For the specific choice of radiating spherical wave functions the approach is illustrated by deriving unitary reducible representations of non-cubic finite point groups in this basis, and by deriving the corresponding explicit symmetry relations of the coefficient matrix. The reducible representations can be reduced by group-theoretical techniques, thus bringing the coefficient matrix into block-diagonal form, which can greatly reduce ill-conditioning problems in numerical applications.     

Target-space duality between simple compact Lie groups and Lie algebras under the Hamiltonian formalism: I. Remnants of duality at the classical level

It has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie groupG with a bi-invariant metric and a generating function suggested in the physics literature, we follow the above line of thought and work out the canonical transformation generated by together with an Ad-invariant metric and a B-field on the associated Lie algebra ofG so thatG and form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation including a careful analysis of its domain and image. The geometry of the T-dual structure on is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper.