87 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
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.
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
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.
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.
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
Mesons in the massive Schwinger model on the light-cone
We investigate mesons in the bosonized massive Schwinger model in the
light-front Tamm-Dancoff approximation in the strong coupling region. We
confirm that the three-meson bound state has a few percent fermion six-body
component in the strong coupling region when expressed in terms of fermion
variables, consistent with our previous calculations. We also discuss some
qualitative features of the three-meson bound state based on the information
about the wave function.Comment: 19 pages, RevTex, included 6 figures which are compressed and
uuencode
Spontaneous symmetry breaking of (1+1)-dimensional theory in light-front field theory (II)
We discuss spontaneous symmetry breaking of (1+1)-dimensional theory
in light-front field theory using a Tamm-Dancoff truncation. We show that, even
though light-front field theory has a simple vacuum state which is an
eigenstate of the full Hamiltonian, the field can develop a nonzero vacuum
expectation value. This occurs because the zero mode of the field must satisfy
an operator valued constraint equation. In the context of (1+1)-dimensional
theory we present solutions to the constraint equation using a
Tamm-Dancoff truncation to a finite number of particles and modes. We study the
behavior of the zero mode as a function of coupling and Fock space truncation.
The zero mode introduces new interactions into the Hamiltonian which breaks the
symmetry of the theory when the coupling is stronger than the critical
coupling.Comment: 25 page
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
Phase Diagram of the Spin-Orbital model on the Square Lattice
We study the phase diagram of the spin-orbital model in both the weak and
strong limits of the quartic spin-orbital exchange interaction. This allows us
to study quantum phase transitions in the model and to approach from both sides
the most interesting intermediate-coupling regime and in particular the
SU(4)-symmetric point of the Hamiltonian. It was suggested earlier by Li et al
[Phys.Rev.Lett. vol. 81, 3527 (1999)] that at this point the ground state of
the system is a plaquette spin-orbital liquid. We argue that the state is more
complex. There is plaquette order, but it is anisotropic: bonds in one
direction are stronger than those in the perpendicular direction. This order is
somewhat similar to that found recently in the frustrated J_1-J_2 Heisenberg
spin model.Comment: 8 pages, 4 Postscript figure
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