1,054 research outputs found
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
Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials
We study a ring cavity filled with a slab of a right-handed material and a
slab of a left-handed material. Both layers are assumed to be nonlinear Kerr
media. First, we derive a model for the propagation of light in a left-handed
material. By constructing a mean-field model, we show that the sign of
diffraction can be made either positive or negative in this resonator,
depending on the thicknesses of the layers. Subsequently, we demonstrate that
the dynamical behavior of the modulation instability is strongly affected by
the sign of the diffraction coefficient. Finally, we study the dissipative
structures in this resonator and reveal the predominance of a two-dimensional
up-switching process over the formation of spatially periodic structures,
leading to the truncation of the homogeneous hysteresis cycle.Comment: 8 pages, 5 figure
Glueball calculations in large-N_c gauge theory
We use the light-front Hamiltonian of transverse lattice gauge theory to
compute from first principles the glueball spectrum and light-front
wavefunctions in the leading order of the 1/N_c colour expansion. We find
0^{++}, 2^{++}, and 1^{+-} glueballs having masses consistent with N_c=3 data
available from Euclidean lattice path integral methods. The wavefunctions
exhibit a light-front constituent gluon structure.Comment: 4 pages, 2 figures, uses macro boxedeps.tex, minor corrections in
revised versio
A New Basis Function Approach to 't Hooft-Bergknoff-Eller Equations
We analytically and numerically investigate the 't Hooft-Bergknoff-Eller
equations, the lowest order mesonic Light-Front Tamm-Dancoff equations for
U(N_C) and SU(N_C) gauge theories. We find the wavefunction can be well
approximated by new basis functions and obtain an analytic formula for the mass
of the lightest bound state. Its value is consistent with the precedent
results.Comment: 16 pages, 3 figure
Colour-Dielectric Gauge Theory on a Transverse Lattice
We investigate in some detail consequences of the effective colour-dielectric
formulation of lattice gauge theory using the light-cone Hamiltonian formalism
with a transverse lattice. As a quantitative test of this approach, we have
performed extensive analytic and numerical calculations for 2+1-dimensional
pure gauge theory in the large N limit. Because of Eguchi-Kawai reduction, one
effectively studies a 1+1-dimensional gauge theory coupled to matter in the
adjoint representation. We study the structure of coupling constant space for
our effective potential by comparing with the physical results available from
conventional Euclidean lattice Monte Carlo simulations of this system. In
particular, we calculate and measure the scaling behaviour of the entire
low-lying glueball spectrum, glueball wavefunctions, string tension, asymptotic
density of states, and deconfining temperature. We employ a new hybrid
DLCQ/wavefunction basis in our calculations of the light-cone Hamiltonian
matrix elements, along with extrapolation in Tamm-Dancoff truncation,
significantly reducing numerical errors. Finally we discuss, in light of our
results, what further measurements and calculations could be made in order to
systematically remove lattice spacing dependence from our effective potential a
priori.Comment: 48 pages, Latex, uses macro boxedeps.tex, minor errors corrected in
revised versio
Tube Model for Light-Front QCD
We propose the tube model as a first step in solving the bound state problem
in light-front QCD. In this approach we neglect transverse variations of the
fields, producing a model with 1+1 dimensional dynamics. We then solve the two,
three, and four particle sectors of the model for the case of pure glue SU(3).
We study convergence to the continuum limit and various properties of the
spectrum.Comment: 29 page
Mesons a in Collinear QCD Model
A phenomenological model for the quark structure of mesons is considered. The
model is based on the tube model for QCD, where all quanta with nonzero
transverse momenta are neglected. In the limit that the mass term of the gluons
goes to infinity, the model is equivalent to a combination of the 't Hooft and
Gross-Neveu models and can be solved semi-analytically. The model has the
properties of confinement, chiral symmetry breaking and asymptotic freedom and
thus resembles QCD in three key respects. Spectra, distribution amplitudes and
form factors of mesons are analyzed.Comment: final version, to appear in PR
Variational Calculation of the Effective Action
An indication of spontaneous symmetry breaking is found in the
two-dimensional model, where attention is paid to the
functional form of an effective action. An effective energy, which is an
effective action for a static field, is obtained as a functional of the
classical field from the ground state of the hamiltonian interacting
with a constant external field. The energy and wavefunction of the ground state
are calculated in terms of DLCQ (Discretized Light-Cone Quantization) under
antiperiodic boundary conditions. A field configuration that is physically
meaningful is found as a solution of the quantum mechanical Euler-Lagrange
equation in the limit. It is shown that there exists a nonzero field
configuration in the broken phase of symmetry because of a boundary
effect.Comment: 26 pages, REVTeX, 7 postscript figures, typos corrected and two
references adde
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