%0 Journal Article %1 Brodsky2004333 %A Brodsky, S.J. %A Franke, V.A. %A Hiller, J.R. %A McCartor, G. %A Paston, S.A. %A Prokhvatilov, E.V. %D 2004 %J Nuclear Physics B %K AMM Light-cone QED quantization %N 1-2 %P 333 - 362 %R DOI: 10.1016/j.nuclphysb.2004.10.027 %T A nonperturbative calculation of the electron's magnetic moment %U http://www.sciencedirect.com/science/article/B6TVC-4DNHHV0-4/2/65904f5c82cef5729fc22e7262ee1ed6 %V 703 %X 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.

@article{Brodsky2004333, 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.}, added-at = {2009-06-27T12:27:51.000+0200}, author = {Brodsky, S.J. and Franke, V.A. and Hiller, J.R. and McCartor, G. and Paston, S.A. and Prokhvatilov, E.V.}, biburl = {https://www.bibsonomy.org/bibtex/29cf25ff751a39ed64a9b5d0b5f28a273/random3f}, description = {ScienceDirect - Nuclear Physics B : A nonperturbative calculation of the electron's magnetic moment}, doi = {DOI: 10.1016/j.nuclphysb.2004.10.027}, interhash = {425e559b69c5283c9c0d1b8a87409bd1}, intrahash = {9cf25ff751a39ed64a9b5d0b5f28a273}, issn = {0550-3213}, journal = {Nuclear Physics B}, keywords = {AMM Light-cone QED quantization}, number = {1-2}, pages = {333 - 362}, timestamp = {2009-06-27T12:43:29.000+0200}, title = {A nonperturbative calculation of the electron's magnetic moment}, url = {http://www.sciencedirect.com/science/article/B6TVC-4DNHHV0-4/2/65904f5c82cef5729fc22e7262ee1ed6}, volume = 703, year = 2004 }