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

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.

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.

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

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

Spin Susceptibility and Gap Structure of the Fractional-Statistics Gas

This paper establishes and tests procedures which can determine the electron energy gap of the high-temperature superconductors using the $t\!-\!J$ model with spinon and holon quasiparticles obeying fractional statistics. A simpler problem with similar physics, the spin susceptibility spectrum of the spin 1/2 fractional-statistics gas, is studied. Interactions with the density oscillations of the system substantially decrease the spin gap to a value of $(0.2 \pm 0.2)$ $\hbar \omega_c$, much less than the mean-field value of $\hbar\omega_c$. The lower few Landau levels remain visible, though broadened and shifted, in the spin susceptibility. As a check of the methods, the single-particle Green's function of the non-interacting Bose gas viewed in the fermionic representation, as computed by the same approximation scheme, agrees well with the exact results. The same mechanism would reduce the gap of the $t\!-\!J$ model without eliminating it.Comment: 35 pages, written in REVTeX, 16 figures available upon request from [email protected]

Variational Calculation of the Effective Action

An indication of spontaneous symmetry breaking is found in the two-dimensional $\lambda\phi^4$ 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 $H[J]$ 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 $J\to 0$ limit. It is shown that there exists a nonzero field configuration in the broken phase of $Z_2$ symmetry because of a boundary effect.Comment: 26 pages, REVTeX, 7 postscript figures, typos corrected and two references adde

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