149 research outputs found
On Signals Imbedded in Noise: Report R-2 (Second Running)
Control Systems Laboratory changed its name to Coordinated Science LaboratoryContract DA-11-022-ORD-17
The diagonalization of quantum field Hamiltonians
We introduce a new diagonalization method called quasi-sparse eigenvector
diagonalization which finds the most important basis vectors of the low energy
eigenstates of a quantum Hamiltonian. It can operate using any basis, either
orthogonal or non-orthogonal, and any sparse Hamiltonian, either Hermitian,
non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part
of a new computational approach which combines both diagonalization and Monte
Carlo techniques.Comment: 12 pages, 8 figures, new material adde
Renormalization of Tamm-Dancoff Integral Equations
During the last few years, interest has arisen in using light-front
Tamm-Dancoff field theory to describe relativistic bound states for theories
such as QCD. Unfortunately, difficult renormalization problems stand in the
way. We introduce a general, non-perturbative approach to renormalization that
is well suited for the ultraviolet and, presumably, the infrared divergences
found in these systems. We reexpress the renormalization problem in terms of a
set of coupled inhomogeneous integral equations, the ``counterterm equation.''
The solution of this equation provides a kernel for the Tamm-Dancoff integral
equations which generates states that are independent of any cutoffs. We also
introduce a Rayleigh-Ritz approach to numerical solution of the counterterm
equation. Using our approach to renormalization, we examine several ultraviolet
divergent models. Finally, we use the Rayleigh-Ritz approach to find the
counterterms in terms of allowed operators of a theory.Comment: 19 pages, OHSTPY-HEP-T-92-01
Six-body Light-Front Tamm-Dancoff approximation and wave functions for the massive Schwinger model
The spectrum of the massive Schwinger model in the strong coupling region is
obtained by using the light-front Tamm-Dancoff (LFTD) approximation up to
including six-body states. We numerically confirm that the two-meson bound
state has a negligibly small six-body component. Emphasis is on the usefulness
of the information about states (wave functions). It is used for identifying
the three-meson bound state among the states below the three-meson threshold.
We also show that the two-meson bound state is well described by the wave
function of the relative motion.Comment: 19 pages, RevTeX, 7 figures are available upon request; Minor errors
have been corrected; Final version to appear in Phys.Rev.
Nuclear forces from chiral Lagrangians using the method of unitary transformation I: Formalism
We construct the two- and three-nucleon potential based on the most general
chiral effective pion-nucleon Lagrangian using the method of unitary
transformations. For that, we develop a power counting scheme consistent with
this projection formalism. In contrast to previous results obtained in
old-fashioned time-ordered perturbation theory, the method employed leads to
energy-independent potentials. We discuss in detail the similarities and
differences to the existing chiral nucleon-nucleon potentials. We also show
that to leading order in the power counting, the three-nucleon forces vanish
lending credit to the result obtained by Weinberg using old-fashioned
time-ordered perturbation theory.Comment: 27 pp, LaTeX file, 8 figures (uses epsf
Flow equations for QED in the light front dynamics
The method of flow equations is applied to QED on the light front. Requiring
that the partical number conserving terms in the Hamiltonian are considered to
be diagonal and the other terms off-diagonal an effective Hamiltonian is
obtained which reduces the positronium problem to a two-particle problem, since
the particle number violating contributions are eliminated. No infrared
divergencies appear. The ultraviolet renormalization can be performed
simultaneously.Comment: 15 pages, Latex, 3 pictures, Submitted to Phys.Rev.
Perturbative Tamm-Dancoff Renormalization
A new two-step renormalization procedure is proposed. In the first step, the
effects of high-energy states are considered in the conventional (Feynman)
perturbation theory. In the second step, the coupling to many-body states is
eliminated by a similarity transformation. The resultant effective Hamiltonian
contains only interactions which do not change particle number. It is subject
to numerical diagonalization. We apply the general procedure to a simple
example for the purpose of illustration.Comment: 20 pages, RevTeX, 10 figure
Nonperturbative renormalization group in a light-front three-dimensional real scalar model
The three-dimensional real scalar model, in which the symmetry
spontaneously breaks, is renormalized in a nonperturbative manner based on the
Tamm-Dancoff truncation of the Fock space. A critical line is calculated by
diagonalizing the Hamiltonian regularized with basis functions. The marginal
() coupling dependence of the critical line is weak. In the broken
phase the canonical Hamiltonian is tachyonic, so the field is shifted as
. The shifted value is determined as a function of
running mass and coupling so that the mass of the ground state vanishes.Comment: 23 pages, LaTeX, 6 Postscript figures, uses revTeX and epsbox.sty. A
slight revision of statements made, some references added, typos correcte
Defining the Force between Separated Sources on a Light Front
The Newtonian character of gauge theories on a light front requires that the
longitudinal momentum P^+, which plays the role of Newtonian mass, be
conserved. This requirement conflicts with the standard definition of the force
between two sources in terms of the minimal energy of quantum gauge fields in
the presence of a quark and anti-quark pinned to points separated by a distance
R. We propose that, on a light front, the force be defined by minimizing the
energy of gauge fields in the presence of a quark and an anti-quark pinned to
lines (1-branes) oriented in the longitudinal direction singled out by the
light front and separated by a transverse distance R. Such sources will have a
limited 1+1 dimensional dynamics. We study this proposal for weak coupling
gauge theories by showing how it leads to the Coulomb force law. For QCD we
also show how asymptotic freedom emerges by evaluating the S-matrix through one
loop for the scattering of a particle in the N_c representation of color
SU(N_c) on a 1-brane by a particle in the \bar N_c representation of color on a
parallel 1-brane separated from the first by a distance R<<1/Lambda_{QCD}.
Potential applications to the problem of confinement on a light front are
discussed.Comment: LaTeX, 15 pages, 12 figures; minor typos corrected; numerical
correction in equation 3.
Structure Preserving Parallel Algorithms for Solving the Bethe-Salpeter Eigenvalue Problem
The Bethe-Salpeter eigenvalue problem is a dense structured eigenvalue
problem arising from discretized Bethe-Salpeter equation in the context of
computing exciton energies and states. A computational challenge is that at
least half of the eigenvalues and the associated eigenvectors are desired in
practice. We establish the equivalence between Bethe-Salpeter eigenvalue
problems and real Hamiltonian eigenvalue problems. Based on theoretical
analysis, structure preserving algorithms for a class of Bethe-Salpeter
eigenvalue problems are proposed. We also show that for this class of problems
all eigenvalues obtained from the Tamm-Dancoff approximation are overestimated.
In order to solve large scale problems of practical interest, we discuss
parallel implementations of our algorithms targeting distributed memory
systems. Several numerical examples are presented to demonstrate the efficiency
and accuracy of our algorithms
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