A nonperturbative calculation of the electron's magnetic moment

Abstract

In principle, the complete spectrum and bound-state wave functions of a quantum field theory can be determined by finding the eigenvalues and eigensolutions of its light-cone Hamiltonian. One of the challenges in obtaining nonperturbative solutions for gauge theories such as QCD using light-cone Hamiltonian methods is to renormalize the theory while preserving Lorentz symmetries and gauge invariance. For example, the truncation of the light-cone Fock space leads to uncompensated ultraviolet divergences. We present two methods for consistently regularizing light-cone-quantized gauge theories in Feynman and light-cone gauges: (1) the introduction of a spectrum of Pauli-Villars fields which produces a finite theory while preserving Lorentz invariance; (2) the augmentation of the gauge-theory Lagrangian with higher derivatives. In the latter case, which is applicable to light-cone gauge (A^+ = 0), the A^- component of the gauge field is maintained as an independent degree of freedom rather than a constraint. Finite-mass Pauli-Villars regulators can also be used to compensate for neglected higher Fock states. As a test case, we apply these regularization procedures to an approximate nonperturbative computation of the anomalous magnetic moment of the electron in QED as a first attempt to meet Feynman's famous challenge.

35 pages, elsart.cls, 3 figures

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Cited by in corpus (29)

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• Nonperturbative light-front Hamiltonian methods
• Basis light-front quantization approach to photon
• On the nonperturbative solution of Pauli--Villars-regulated light-front QED: A comparison of the sector-dependent and standard parameterizations
• Generalized parton distributions in a light-front nonperturbative approach
• A nonperturbative calculation of the electron's magnetic moment with truncation extended to two photons
• Transverse structure of electron in momentum space in basis light-front quantization
• Two-boson truncation of Pauli-Villars-regulated Yukawa theory
• Regularization of fermion self-energy and electromagnetic vertex in Yukawa model within light-front dynamics
• Advances in Basis Light-front Quantization
• Nonperturbative Pauli-Villars regularization of vacuum polarization in light-front QED
• A first nonperturbative calculation in light-front QED for an arbitrary covariant gauge
• Restoration of the chiral limit in Pauli-Villars-regulated light-front QED
• Infra-red Divergences in Light-Front QED and Coherent State Basis
• Fermion Self Energy Correction in Light-Front QED using Coherent State Basis
• Renormalized Light Front Hamiltonian in the Pauli-Villars Regularization
• Hamiltonian Light-Front Field Theory: Recent Progress and Tantalizing Prospects
• Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
• Nonperturbative light-front effective potential for static sources in quenched scalar Yukawa theory
• Pauli-Villars regularization of non-Abelian gauge theories
• Construction of Perturbatively Correct Light Front Hamiltonian for (2+1)-Dimensional Gauge Theory
• Feynman perturbation theory for gauge theory on transverse lattice
• Lepton Generation Problem, Some Properties and Implications of the Curved Spacetime Dirac Equation -- (II)
• A light-front coupled cluster method
• Perturbative Formulation of Pure Space-Like Axial Gauge QED with Infrared Divergences Regularized by Residual Gauge Fields
• Nonperturbative solution of Yukawa theory and gauge theories