Light-Front Quantization and QCD Phenomena

Abstract

The light-front quantization of QCD provides an alternative to lattice gauge theory for computing the mass spectrum, scattering amplitudes, and other physical properties of hadrons directly in Minkowski space. Nonperturbative light-front methods for solving gauge theory and obtaining light-front wavefunctions, such as discretized light-front quantization, the transverse lattice, and light-front resolvents are reviewed. The resulting light-front wavefunctions give a frame-independent interpolation between hadrons and their quark and gluon degrees of freedom, including an exact representation of spacelike form factors, transition form factors such as B → ℓνπ, and generalized parton distributions. In the case of hard inclusive reactions, the effects of final-state interactions must be included in order to interpret leading-twist diffractive contributions, nuclear shadowing, and single-spin asymmetries. I also discuss how the AdS/CFT correspondence between string theory and conformal gauge theory can be used to constrain the form and power-law fall-off of the light-front wavefunctions. In the case of electroweak theory, light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field, leaving the light-front vacuum equal to the perturbative vacuum.

Light front Hamiltonian formulation of QED and some tree level applications

“…It should be stressed that although the motivation for the LF coordinate system came initially from considerations of infinite momentum frame; it is not necessary to restrict oneself to this particular frame. Viewed as essentially a change of variables one has a clearly fully relativistic field theory with the added benefit of a simplified vacuum structure [6].…”

“…There is a large body of work relating to LF formulation of QCD as can be seen from the references attached to the review presented by Brodsky [6] but little directly to QED. Most of the LF formulations maintain explicit covariance and adopt the Mandelstam-Leibbrandt [18,19] prescription for the handling of infrared problems arising from the modifications to the gauge field propagator.…”