We consider the constrained zero modes found in the application of discrete light-cone quantization (DLCQ) to the nonperturbative solution of quantum field theories. These modes are usually neglected for simplicity, but we show that their inclusion can be relatively straightforward, and, what is more, that they are useful for nonperturbative calculations of field-theoretic spectra. In particular, inclusion of zero modes improves the convergence of the numerical calculation and makes possible the direct calculation of vacuum expectation values, even when the zero modes are determined dynamically. We also comment on zero-mode contributions not included by DLCQ, namely zero-mode loops.Comment: 10 pages, LaTeX/REVTeX, no figures; typos corrected, references added, discussion of zero-mode loops adde
We study the lowest-mass eigenstates of φ 4 1+1 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-squaredcase. An apparent discrepancy with equal-time calculations of the critical coupling is resolved by an appropriate mass renormalization.
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 selfenergy effects obtained from a two-photon truncation are enough to bring the standard-parameterization result for the anomalous moment into agreement * Corresponding author Email address: jhiller@d.umn.edu (John R. Hiller) February 21, 2018 with experiment within numerical errors. This continues the development of a method for the nonperturbative solution of strongly coupled theories, in particular quantum chromodynamics. Preprint submitted to Annals of Physics
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.
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