Light-front-quantized QCD in the light-cone gauge: The doubly transverse gauge propagator

Abstract

The light-front ͑LF͒ quantization of QCD in the light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high-momentum transfer inclusive and exclusive reactions. We present a systematic study of LF-quantized gauge theory following the Dirac method, and construct a Dyson-Wick S-matrix expansion based on LF time-ordered products. The free theory gauge field is shown to satisfy the Lorentz condition as an operator equation as well as the light-cone gauge condition. Its propagator is found to be transverse with respect to both its 4 momentum and the gauge direction. The interaction Hamiltonian of QCD can be expressed in a form resembling that of covariant theory, except for additional instantaneous interactions which can be treated systematically. The renormalization constants in YM theory are shown to satisfy the identity Z 1 ϭZ 3 at one-loop order. The QCD ␤ function, computed in the noncovariant light-cone gauge, agrees with that known in the conventional framework. Some comments are also made about the relationship of our LF framework, with a doubly transverse gauge propagator, to the analytic effective charge and renormalization scheme defined by the pinch technique, the unitarity relations, and the spectral representation. LF quantization thus provides a consistent formulation of gauge theory, despite the fact that the hyperplanes x Ϯ ϭ0 used to impose boundary conditions constitute characteristic surfaces of a hyperbolic partial differential equation.

Heavy-to-light form factors on the light cone

“…The Feynman rules for ξ and A ⊥ have been derived, such as in [33] which are not useful for our purpose. We prefer to use another formulation given in [25].…”

Spin decomposition of the electron in QED

“…In general, the extra term proportional to k 2 in Eq. (52) is compensated for by an instantaneous interaction in the light-front Hamiltonian, which comes from eliminating the non-dynamical field A − in terms of the dynamical ones in the light-cone gauge (there is also an instantaneous fermion propagator in light-front quantization, but it does not contribute here) [23]. Therefore, to do calculations one can either use the photon propagator in Eq.…”

Light-Front Quantization and QCD Phenomena

“…It contains the usual Dirac interactions between the quarks and gluons, the three-point and four-point gluon non-Abelian interactions, plus instantaneous gluon exchange and quark exchange contributions. The renormalization constants in the non-Abelian theory have been shown [15] to satisfy the identity Z 1 = Z 3 at one-loop order and are independent of the reference direction n µ . The QCD β function has also been computed at one loop [15].…”

“…The renormalization constants in the non-Abelian theory have been shown [15] to satisfy the identity Z 1 = Z 3 at one-loop order and are independent of the reference direction n µ . The QCD β function has also been computed at one loop [15]. Dimensional regularization and the Mandelstam-Leibbrandt prescription [16,17,18] for LC gauge can be used to define the Feynman loop integrations [19].…”

“…In 3 + 1 dimensions, the transverse field A ⊥ propagates massless spin-one gluon quanta with polarization vectors [14] which satisfy both the gauge condition ǫ + λ = 0 and the Lorentz condition k · ǫ = 0. The interaction Hamiltonian of QCD in light-cone gauge can be derived by systematically applying the Dirac bracket method to identify the independent fields [12,15]. It contains the usual Dirac interactions between the quarks and gluons, the three-point and four-point gluon non-Abelian interactions, plus instantaneous gluon exchange and quark exchange contributions.…”