A nonperturbative calculation of the electron's magnetic moment
Abstract
In principle, the complete spectrum and boundstate wave functions of a quantum field theory can be determined by finding the eigenvalues and eigensolutions of its lightcone Hamiltonian. One of the challenges in obtaining nonperturbative solutions for gauge theories such as QCD using lightcone Hamiltonian methods is to renormalize the theory while preserving Lorentz symmetries and gauge invariance. For example, the truncation of the lightcone Fock space leads to uncompensated ultraviolet divergences. We present two methods for consistently regularizing lightconequantized gauge theories in Feynman and lightcone gauges: (1) the introduction of a spectrum of PauliVillars fields which produces a finite theory while preserving Lorentz invariance; (2) the augmentation of the gaugetheory Lagrangian with higher derivatives. In the latter case, which is applicable to lightcone gauge ( A=0), the A component of the gauge field is maintained as an independent degree of freedom rather than a constraint. Finitemass PauliVillars 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.
 Publication:

Nuclear Physics B
 Pub Date:
 December 2004
 DOI:
 10.1016/j.nuclphysb.2004.10.027
 arXiv:
 arXiv:hepph/0406325
 Bibcode:
 2004NuPhB.703..333B
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 35 pages, elsart.cls, 3 figures