A Nonperturbative Calculation of the Electron's Magnetic Moment

Technical Report · Fri Jun 25 04:00:00 EDT 2004

DOI:https://doi.org/10.2172/827007· OSTI ID:827007

Brodsky, S ^[1]

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1. SLAC

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{sup +} = 0), the A{sup -} 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.

• Research Organization: Stanford Linear Accelerator Center, Menlo Park, CA (US)
• Sponsoring Organization: USDOE Office of Science (US)
• DOE Contract Number: AC03-76SF00515
• OSTI ID: 827007
• Report Number(s): SLAC-PUB-10506
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
EIGENVALUES
ELECTRONS
GAUGE INVARIANCE
HAMILTONIANS
LAGRANGIAN FUNCTION
LIGHT CONE
LORENTZ INVARIANCE
MAGNETIC MOMENTS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
ULTRAVIOLET DIVERGENCES
WAVE FUNCTIONS