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.
Description
ScienceDirect - Nuclear Physics B : A nonperturbative calculation of the electron's magnetic moment
%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
}