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.
Bibliographical noteFunding Information:
This work was supported by the Department of Energy through contracts DE-AC03-76SF00515 (S.J.B.), DE-FG02-98ER41087 (J.R.H.), and DE-FG03-95ER40908 (G.M.) and by the Russian Foundation of Fundamental Investigations (S.A.P. and E.V.P.).
Work supported in part by the Department of Energy under contract Nos. DE-AC03-76SF00515, DE-FG02-98ER41087, and DE-FG03-95ER40908, and by the Russian Foundation of Fundamental Investigations.