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Pole-factorization theorem in quantum electrodynamics

Description: In quantum electrodynamics a classical part of the S-matrix is normally factored out in order to obtain a quantum remainder that can be treated perturbatively without the occurrence of infrared divergences. However, this separation, as usually performed, introduces spurious large-distance effects that produce an apparent breakdown of the important correspondence between stable particles and poles of the S-matrix, and, consequently, lead to apparent violations of the correspondence principle and to incorrect results for computations in the mesoscopic domain lying between the atomic and classical regimes. An improved computational technique is described that allows valid results to be obtained in this domain, and that leads, for the quantum remainder, in the cases studied, to a physical-region singularity structure that, as regards the most singular parts, is the same as the normal physical-region analytic structure in theories in which all particles have non-zero mass. The key innovations here are to define the classical part in coordinate space, rather than in momentum space, and to define there a separation of the photon-electron coupling into its classical and quantum parts that has the following properties: (1) The contributions from the terms containing only classical couplings can be summed to all orders to give a unitary operator that generates the coherent state that corresponds to the appropriate classical process, and (2) The quantum remainder can be rigorously shown to exhibit, as regards its most singular parts, the normal analytic structure. 22 refs.
Date: January 1, 1996
Creator: Stapp, H.P.
Partner: UNT Libraries Government Documents Department

Chemical reaction rates using the semiclassical Van-Vleck initialvalue representation

Description: A semiclassical IVR formulation using the Van-Vleck propagator has been used to calculate the flux correlation function and thereby reaction rate constants. This Van-Vleck formulation of the flux-flux correlation function is computationally as simple as the classical Wigner model. However unlike the latter, it has the ability to capture quantum interference/coherence effects. Classical trajectories are evolved starting from the dividing surface that separates reactants and products, and are evolved negatively in time. This formulation has been tested on model problems ranging from the Eckart barrier, double well to the collinear H + H{sub 2}.
Date: November 29, 2006
Creator: Venkataraman, Charulatha & Miller, William H.
Partner: UNT Libraries Government Documents Department

Further results about field theory on the world sheet and stringformation

Description: The present article is the continuation of the earlier work, which used the world sheet representation and the mean field approximation to sum planar graphs in massless {phi}{sup 3} field theory. The authors improve on the previous work in two respects: A prefactor in the world sheet propagator that had been neglected is now taken into account. In addition, they introduce a non-zero bare mass for the field {phi}. Working with a theory with cutoff and using the mean field approximation, they find that, depending on the range of values of the mass and coupling constant, the model has two phases: A string forming phase and a perturbative field theory phase. They also find the generation of a new degree of freedom, which was not in the model originally. This new degree of freedom can be thought of as the string slope, which is now promoted into a fluctuating dynamical variable. Finally, they show that the introduction of the bare mass makes it possible to renormalize the model.
Date: January 15, 2005
Creator: Bardakci, Korbut
Partner: UNT Libraries Government Documents Department

Hole-Coupled Resonators Tunable Infrared Free Electron Lasers

Description: We review the study of hole-coupled resonators for broadly tunable free electron laser (FEL) applications. The mode profiles inside and outside the cavity, the diffraction losses at the mirror edges and intracavity apertures, the amount of useful power coupled through the holes, and the FEL gain are calculated for several dominant azimuthal and radial modes. The FEL interaction is taken into account by constructing a propagator similar to the Fresnel integral for free space propagation. It is found that non-confocal resonators can provide efficient hole coupling over a broad wavelength range, as long as the mode beating caused by a degeneracy in the round trip loss can be avoided. The degeneracy between the azimuthally symmetric class of modes is removed by FEL interaction, and the azimuthally asymmetric modes can be suppressed by means of intracavity apertures. Therefore, in a nonconfocal configuration, a hole-coupled resonator can be designed that is tunable over a broad range of wavelength by employing an adjustable intracavity aperture. On the other hand, confocal resonators are not suitable for hole coupling; Although mode beating does not occur in a confocal resonator, the hole coupling is difficult because the modes tend to avoid the hole. We provide a simple physical understanding of the difference in the performance of the confocal and non-confocal resonators. We also calculate and analyze the mode content of an empty resonator under continuous external mode injection. Such calculation is useful in interpreting experiments testing the hole coupling performance using CW lasers.
Date: February 1, 1993
Creator: Xie, M. & Kim, K.-J.
Partner: UNT Libraries Government Documents Department

Time-dependent simulations of large-scale quantum mechanical processes

Description: Time dependent linear and nonlinear equations govern the evolution of an extensive set of physical systems and processes describing, to enumerate just a few, Bose-Einstein condensates; soliton propagation in optical and photonic band-gap fibers; quantum control of atomic and molecular collisions and reactions; highly-compressed liquids; and dense and ultracold plasmas. While the media vary substantially, the basic computational procedures have many common features. We focus on the nonlinear Schrodinger equation and discuss two powerful approaches to its propagation: the Arnoldi/Lanczos(AL)l and Real Space Product Formula(RSPF)2. Both provide efficient systematic approximations to the short-time exponential propagator that moves the solution between time steps. We implement the former in a discrete variable representation (DVR)3 both in spatial grid and finite element forms and the latter in a spatial mesh with a finite difference representation of the kinetic energy operator. Both approaches require O(N) operations to propagate the wavefunction between time steps and handle multidimensional systems. We shall also draw connections with Liouville formulations used in quantum molecular dynamics simulations of large collections of atoms and molecules. After briefly outlining these formulations, we shall discuss some of the varied applications.
Date: January 1, 2002
Creator: Collins, L. A. (Lee A.)
Partner: UNT Libraries Government Documents Department

Meson spectrum from the Bethe-Salpeter equation

Description: We present details of a model for calculating the mass spectrum of light-quark mesons and decay constants of the pseudoscalar meson octet from a phenomenological model based on Dyson-Schwinger and Bethe-Salpeter equations. In this model the Bethe-Salpeter kernel is approximated by a separable ansatz obtained from input quark propagators. 13 refs., 2 tabs.
Date: January 22, 1996
Creator: Burden, C. J.; Qian, L.; Tandy, P. C.; Roberts, C. D. & Thomson, M. J.
Partner: UNT Libraries Government Documents Department

Analysis of Errors in a Special Perturbations Satellite Orbit Propagator

Description: We performed an analysis of error densities for the Special Perturbations orbit propagator using data for 29 satellites in orbits of interest to Space Shuttle and International Space Station collision avoidance. We find that the along-track errors predominate. These errors increase monotonically over each 36-hour prediction interval. The predicted positions in the along-track direction progressively either leap ahead of or lag behind the actual positions. Unlike the along-track errors the radial and cross-track errors oscillate about their nearly zero mean values. As the number of observations per fit interval decline the along-track prediction errors, and amplitudes of the radial and cross-track errors, increase.
Date: February 1, 1999
Creator: Beckerman, M. & Jones, J.P.
Partner: UNT Libraries Government Documents Department

Confinement and the analytic structure of the one body propagator in scalar QED

Description: The authors investigate the behavior of the one body propagator in SQED. The self energy is calculated using three different methods: (1) the simple bubble summation, (2) the Dyson-Schwinger equation, and (3) the Feynman-Schwinger representation. The Feynman-Schwinger representation allows an exact analytical result in the quenched approximation. It is shown that, while the exact result produces a real mass pole for all couplings, the bubble sum and the Dyson-Schwinger approach in rainbow approximation leads to complex mass poles beyond a certain critical coupling. The model exhibits confinement as a basic property of the four-point function without implying a lack of a mass pole in the propagator.
Date: June 1, 1999
Creator: Savkli, C.; Tjon, J. & Gross, F.
Partner: UNT Libraries Government Documents Department

Fast 3-D seismic modeling and prestack depth migration using generalized screen methods. Final report for period January 1, 1998 - December 31, 2000

Description: Completed a theoretical analysis of phase screen propagators to answer several critical questions: the existence of a singularity in the Green's function for the case of a zero vertical wavenumber, the stability and accuracy of such propagators, and the effects of backscattering for large contrast heterogeneous media. The theory is based on separating the wavefield into forescattering and backscattering parts. The approach is robust and appropriate for earth structures with high velocity contrast. This theory also resolves the apparent singularity problem that has persisted in generalized screen propagator formulations. With this formulation we studied the effects of the commonly used approximations as a function of the degree of velocity contrast in the media.
Date: March 31, 2001
Creator: Toksoz, M. Nafi
Partner: UNT Libraries Government Documents Department

Quark and proton spin structure in the Instanton Liquid Model of QCD

Description: Within an instanton based model of QCD the authors address the important question of how much of the proton spin is carried by the spins of the quarks and how much is due to orbital angular momentum and the spins of the gluons. Since this question arises already on the level of a single quark inside the proton, they study axial vector correlation functions for a quark in the so called Random Instanton Liquid Model (RILM) as well as for the Interacting Instanton Liquid Model (IILM).
Date: December 1, 1997
Creator: Blotz, A. & Shuryak, E.
Partner: UNT Libraries Government Documents Department

t-Channel unitarity construction of small-x kernels

Description: In the leading-log approximation, the small-x behavior of parton distributions in QCD is derived from the BFKL evolution equation. The authors describe the ion as a reggeon Bethe-Salpeter equation and discuss the use of reggeon diagrams to obtain 2-2 and 2-4 reggeon interactions at O(g{sup 4}). They then outline the dispersion theory basis of multiparticle j-plane analysis and describe how a gauge theory can be studied by combining Ward identity constraints with the group structure of reggeon interactions. Gluon reggeization, the O(g{sup 2}) BFKL kernel and O(g{sup 4}) corrections to it, are derived within this formalism. They give an explicit expression for the O(g{sup 4}) forward ``parton`` kernel in terms of logarithms and evaluate the eigenvalues. A separately infra-red finite component with a holomorphically factorizable spectrum is shown to be present and conjectured to be a new leading-order partial-wave amplitude. A comparison is made with Kirschner`s discussion of O(g{sup 4}) contributions from the multi-Regge effective action.
Date: 1994-12~
Creator: Coriano, C. & White, A. R.
Partner: UNT Libraries Government Documents Department

Pion-nucleon scattering in P{sub 11} channel and the Roper resonance

Description: The {pi}N scattering in P{sub 11} channel is investigated within the two-channel model of Pearce and Afnan. The model consists of: (1) vertex interactions b {yields} {pi}N, {pi}{nabla} with b denoting either a bare nucleon or a bare Roper state, (2) a background potential {upsilon}{sub {pi}B,{pi}B} with B = N,{nabla}. Assuming that {upsilon}{sub {pi}B,{pi}B} can be phenomenologically parameterized as a separable form and the {pi}N inelasticity can be accounted for by dressing the {nabla} in the {pi}{nabla} channel by a {nabla} {leftrightarrow} {pi}N vertex, it is found that the fit to the P{sub 11} phase shifts up to 1 GeV favors a large mass of the bare Roper state. Our results are consistent with the findings of Pearce and Afnan that if the mass of the bare Roper state is restricted to be {le}1600 MeV, then a physical Roper will have a width which is too narrow causing a rapid variation of the phase shifts at energies near the resonance energy.
Date: March 1996
Creator: Bugaev, K. A.; Yang, Shin Nan & Lee, T. S. H.
Partner: UNT Libraries Government Documents Department

Discrete anomaly and dynamical mass in 2+1 dimension U(1){sub v} {times} U(1){sub A} model

Description: The authors note that in (2+1)-dimensional gauge theories with even number of massless fermions, there is anomalous Z{sub 2} symmetry if theory is regularized in a parity-invariant way. They then consider a parity invariant U(1){sub v} {times} U(1){sub A} model, which induces a mutual Chern-Simons term in the effective action due to Z{sub 2} anomaly. The effect of the discrete anomaly is studied in the induced spin and in the dynamical fermion mass.
Date: December 31, 1995
Creator: Hong, D.K.
Partner: UNT Libraries Government Documents Department

A continuum order parameter for deconfinement

Description: Dyson-Schwinger equations are presented as a non-perturbative tool for the study and modeling of QCD at finite-{ital T}. An order parameter for deconfinement, applicable for both light and heavy quarks, is introduced. In a simple Dyson-Schwinger equation model of two-flavor QCD, coincident, 2nd-order chiral symmetry restoration and deconfinement transitions occur at {ital T} {approx} 150 MeV, with the same critical exponent, {Beta} {approx} 0.33.
Date: March 1, 1997
Creator: Roberts, C.D.
Partner: UNT Libraries Government Documents Department

Extended pseudo-screen migration with multiple reference velocities

Description: The pseudo-screen propagator is a kind of one way wave propagation based on the local Born approximation. The problem of the propagator is that it is difficult to calculate the scattered fields when the velocity perturbation is large; not to mention the accuracy of the propagator. We develop an extended pseudo-screen propagator by introducing different reference velocities in different regions of a medium to ensure the condition of small perturbation. The exploding reflector data for a 2D slice of the SEG/EAEG 3D salt model is generated by a finite difference scheme to test the feasibility of the method. The migration result demonstrates that the method can handle severe lateral velocity variations and provides high quality images for complex structures.
Date: November 1, 1997
Creator: Huang, Lian-Jie & Fehler, M.C.
Partner: UNT Libraries Government Documents Department

The quark and meson structure in the instanton liquid model

Description: Within an instanton based model of QCD the authors address the important question of how much of the proton spin is carried by the spins of the quarks and how much is due to orbital angular momentum and the spins of the gluons. Since this question arises already on the level of a single quark inside the proton, they study the axial vector correlation function as well as the anomaly correlator for quarks in the so called Random Instanton Liquid Model (RILM) as well as for the Interacting Instanton Liquid Model (IILM).
Date: December 31, 1997
Creator: Blotz, A. & Shuryak, E.
Partner: UNT Libraries Government Documents Department

Deconfinement and Hadron Properties at Extremes of Temperature and Density

Description: After introducing essential, qualitative concepts and results, the authors discuss the application of Dyson-Schwinger equations to QCD at finite T and {mu}. They summarize the calculation of the critical exponents of two-light-flavor QCD using the chiral and thermal susceptibilities; and an algebraic model that elucidates the origin of an anticorrelation between the {mu}- and T-dependence of a range of meson properties. That model also provides an algebraic understanding of why the finite-T behavior of bulk thermodynamic properties is mirrored in their {mu}-dependence, and why meson masses decrease with {mu} even though f{sub {pi}} and {minus}<{anti q}q> increase. The possibility of diquark condensation is canvassed. Its realization is uncertain because it is contingent upon an assumption abut the quark-quark scattering kernel that is demonstrably false in some applications; e.g., it predicts the existence of colored diquarks in the strong interaction spectrum, which are not observed.
Date: August 1, 1998
Creator: Blaschke, D. & Roberts, C. D.
Partner: UNT Libraries Government Documents Department

Nonperturbative QCD With Modern Tools

Description: In these lectures the author introduces and explores a range of topics of contemporary interest in hadronic physics: from what drives the formation of a nonzero quark condensate to the effect that mechanism has on light and heavy meson form factors and the properties of the quark-gluon plasma. The trail leads naturally through a discussion of confinement, dynamical chiral symmetry breaking and bound state structure: phenomena that require nonperturbative methods for their explanation. In all of this, the necessary and necessarily momentum-dependent modification of the quark and gluon propagators plays a significant role.
Date: July 1, 1998
Creator: Roberts, C. D.
Partner: UNT Libraries Government Documents Department

Vertex Sensitivity in the Schwinger-Dyson Equations of QCD

Description: The nonperturbative gluon and ghost propagators in Landau gauge QCD are obtained using the Schwinger-Dyson equation approach. The propagator equations are solved in Euclidean space using Landau gauge with a range of vertex inputs. Initially we solve for the ghost alone, using a model gluon input, which leads us to favour a finite ghost dressing in the nonperturbative region. In order to then solve the gluon and ghost equations simultaneously, we find that non-trivial vertices are required, particularly for the gluon propagator in the small momentum limit. We focus on the properties of a number vertices and how these differences influence the final solutions. The self-consistent solutions we obtain are all qualitatively similar and contain a mass-like term in the gluon propagator dressing in agreement with related studies, supporting the long-held proposal of Cornwall.
Date: January 1, 2012
Creator: David J. Wilson, Michael R. Pennington
Partner: UNT Libraries Government Documents Department