A nonperturbative calculation of the electron's magnetic moment

• Published in: Nuclear physics. B Vol. 703; no. 1; pp. 333 - 362
• Main Authors: Brodsky, S.J., Franke, V.A., Hiller, J.R., McCartor, G., Paston, S.A., Prokhvatilov, E.V.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 20-12-2004
• Subjects: Light-cone quantization; Mass renormalization; Pauli–Villars regularization; QED; 11.10.Gh; QED; Mass renormalization; 11.15.Tk; Light-cone quantization; Pauli–Villars regularization; 12.38.Lg
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/j.nuclphysb.2004.10.027

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.