We study the lowest-mass eigenstates of ϕ1+14 theory with both odd and even numbers of constituents. The calculation is carried out as a diagonalization of the light-front Hamiltonian in a Fock-space ...representation. In each Fock sector a fully symmetric polynomial basis is used to represent the Fock wave function. Convergence is investigated with respect to the number of basis polynomials in each sector and with respect to the number of sectors. The dependence of the spectrum on the coupling strength is used to estimate the critical coupling for the positive-mass-squared case. An apparent discrepancy with equal-time calculations of the critical coupling is resolved by an appropriate mass renormalization.
We explore the convergence of the light-front coupled-cluster (LFCC) method in the context of two-dimensional quenched scalar Yukawa theory. This theory is simple enough for higher-order LFCC ...calculations to be relatively straightforward. The quenching is to maintain stability; the spectrum of the full theory with pair creation and annihilation is unbounded from below. The basic interaction in the quenched theory is only emission and absorption of a neutral scalar by the complex scalar. The LFCC method builds the eigenstate with one complex scalar and a cloud of neutrals from a valence state that is just the complex scalar and the action of an exponentiated operator that creates neutrals. The lowest order LFCC operator creates one; we add the next order, a term that creates two. At this order there is a direct contribution to the wave function for two neutrals and one complex scalar and additional contributions to all higher Fock wave functions from the exponentiation. Results for the lowest order and this new second-order approximation are compared with those obtained with standard Fock-state expansions. The LFCC approach is found to allow representation of the eigenstate with far fewer functions than the number of wave functions required in a converged Fock-state expansion.
As an extension of recent work on two-dimensional light-front ϕ4 theory, we implement Fock-sector dependence for the bare mass. Such dependence should have important consequences for the convergence ...of nonperturbative calculations with respect to the level of Fock-space truncation. The truncation forces the self-energy corrections to be sector dependent; in particular, the highest sector has no self-energy correction. Thus, the bare mass can be considered sector dependent as well. We find that, although higher Fock sectors have a larger probability, the mass of the lightest state and the value of the critical coupling are not significantly affected. This implies that coherent states or the light-front coupled-cluster method may be required to properly represent critical behavior.
We construct a Schrödinger-like equation for the longitudinal wave function of a meson in the valence qq̄ sector, based on the ’t Hooft model for large-N two-dimensional QCD, and combine this with ...the usual transverse equation from light-front holographic QCD, to obtain a model for mesons with massive quarks. The computed wave functions are compared with the wave function ansatz of Brodsky and de Téramond and used to compute decay constants and parton distribution functions. The basis functions used to solve the longitudinal equation may be useful for more general calculations of meson states in QCD.
•Provide relativistic quark model based on light-front holographic QCD.•Incorporate dependence on quark mass.•Consistent with the Brodsky–de Téramond quark-wave-function ansatz.•Compute meson decay constants and parton distribution functions.•Illustrate use of basis functions that could be convenient for more general numerical calculations in light-front QCD.
We propose a new method for the nonperturbative solution of quantum field theories and illustrate its use in the context of a light-front analog to the Greenberg–Schweber model. The method is based ...on light-front quantization and uses the exponential-operator technique of the many-body coupled-cluster method. The formulation produces an effective Hamiltonian eigenvalue problem in the valence Fock sector of the system of interest, combined with nonlinear integral equations to be solved for the functions that define the effective Hamiltonian. The method avoids the Fock-space truncations usually used in nonperturbative light-front Hamiltonian methods and, therefore, does not suffer from the spectator dependence, Fock-sector dependence, and uncanceled divergences caused by such truncations.
The light-front coupled-cluster (LFCC) method is a technique for solving Hamiltonian eigenvalue problems in light-front-quantized field theories. Its primary purpose is to provide a systematic ...sequence of solvable approximations to the original eigenvalue problem without the truncation of Fock space. Here we discuss the incorporation of zero modes, modes of zero longitudinal momentum, into the formalism of the method. Without zero modes, the light-front vacuum is trivial, and the vacuum expectation value of the field is always zero. The LFCC method with zero modes provides for vacuum structure, in the form of a generalized coherent state of zero modes, as is illustrated here in two-dimensional model field theories.
•Extends the light-front coupled-cluster method to include zero modes.•Illustrates with an analysis of vacuum structure for phi-3, phi-4, and Wick–Cutkosky model field theories.•Demonstrates the applicability of the LFCC method to theories with spontaneous symmetry breaking.
We use the interpolating coordinates studied by Hornbostel to investigate a transition from equal-time quantization to light-front quantization, in the context of two-dimensional ϕ4 theory. A ...consistent treatment is found to require careful consideration of vacuum bubbles, in a nonperturbative extension of the analysis by Collins. Numerical calculations of the spectrum at fixed box size are shown to yield results equivalent to those of equal-time quantization, except when the interpolating coordinates are pressed toward the light-front limit. In that regime, a fixed box size is inconsistent with an accurate representation of vacuum-bubble contributions and causes a spurious divergence in the spectrum. The light-front limit instead requires the continuum momentum-space limit of infinite box size. The calculation of the vacuum energy density is then shown to be independent of the interpolation parameter, which implies that the light-front limit yields the same spectrum as an equal-time calculation. This emphasizes the importance of zero modes and near-zero modes in a light-front analysis of any theory with nontrivial vacuum structure.
We consider quantum electrodynamics quantized on the light front in Feynman gauge and regulated in the ultraviolet by the inclusion of massive, negative-metric Pauli–Villars (PV) particles in the ...Lagrangian. The eigenstate of the electron is approximated by a Fock-state expansion truncated to include one photon. The Fock-state wave functions are computed from the fundamental Hamiltonian eigenvalue problem and used to calculate the anomalous magnetic moment, as a point of comparison. Two approaches are considered: a sector-dependent parameterization, where the bare parameters of the Lagrangian are allowed to depend on the Fock sectors between which the particular Hamiltonian term acts, and the standard choice, where the bare parameters are the same for all sectors. Both methods are shown to require some care with respect to ultraviolet divergences; neither method can allow all PV masses to be taken to infinity. In addition, the sector-dependent approach suffers from an infrared divergence that requires a nonzero photon mass; due to complications associated with this divergence, the standard parameterization is to be preferred. We also show that the self-energy effects obtained from a two-photon truncation are enough to bring the standard-parameterization result for the anomalous moment into agreement with experiment within numerical errors. This continues the development of a method for the nonperturbative solution of strongly coupled theories, in particular quantum chromodynamics.
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