RPA for Light-Front Hamiltonian Field Theory

A self-consistent random phase approximation (RPA) is proposed as an effective Hamiltonian method in Light-Front Field Theory (LFFT). We apply the general idea to the light-front massive Schwinger model to obtain a new bound state equation and solve it numerically.Comment: A major revision in presentation, while the results essentially unchanged. 2 figs. replaced, 1 fig. added, some parts of Sec. V moved to Sec. IV, some wording changed, typos correcte

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.

Fermion Condensates and the Trivial Vacuum of Light-Cone Quantum Field Theory

We discuss the definition of condensates within light-cone quantum field theory. As the vacuum state in this formulation is trivial, we suggest to abstract vacuum properties from the particle spectrum. The latter can in principle be calculated by solving the eigenvalue problem of the light-cone Hamiltonian. We focus on fermionic condensates which are order parameters of chiral symmetry breaking. As a paradigm identity we use the Gell-Mann-Oakes-Renner relation between the quark condensate and the observable pion mass. We examine the analogues of this relation in the `t~Hooft and Schwinger model, respectively. A brief discussion of the Nambu-Jona-Lasinio model is added.Comment: 14 pages, no figures, latex2

Dynamics of the Light-Cone Zero Modes: Theta Vacuum of the Massive Schwinger Model

The massive Schwinger model is quantized on the light cone with great care on the bosonic zero modes by putting the system in a finite (light-cone) spatial box. The zero mode of $A_{-}$ survives Dirac's procedure for the constrained system as a dynamical degree of freedom. After regularization and quantization, we show that the physical space condition is consistently imposed and relates the fermion Fock states to the zero mode of the gauge field. The vacuum is obtained by solving a Schr\"odinger equation in a periodic potential, so that the theta is understood as the Bloch momentum. We also construct a one-meson state in the fermion-antifermion sector and obtained the Schr\"odinger equation for it.Comment: 23 pages, RevTex, no figure

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

Convergence of Discretized Light Cone Quantization in the small mass limit

I discuss the slow convergence of Discretized Light Cone Quantization (DLCQ) in the small mass limit and suggest a solution.Comment: 8 pages, 5 Postscript figures, uses boxedeps.te

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

A New Finite-lattice study of the Massive Schwinger Model

A new finite lattice calculation of the low lying bound state energies in the massive Schwinger model is presented, using a Hamiltonian lattice formulation. The results are compared with recent analytic series calculations in the low mass limit, and with a new higher order non-relativistic series which we calculate for the high mass limit. The results are generally in good agreement with these series predictions, and also with recent calculations by light cone and related techniques

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

The Influence of Higher Fock States in Light-Cone Gauge Theories

In the light-cone Fock state expansion of gauge theories, the influence of non-valence states may be significant in precision non-perturbative calculations. In two-dimensional gauge theories, it is shown how these states modify the behaviour of the light-cone wavefunction in significant ways relative to endemic choices of variational ansatz. Similar effects in four-dimensional gauge theories are briefly discussed.Comment: 4 pages, REVTE