Light-Front-Quantized QCD in Light-Cone Gauge

The light-front (LF) quantization of QCD in 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 the Dyson-Wick S-matrix expansion based on LF-time-ordered products. The 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 four-momentum and the gauge direction. The propagator of the dynamical ψ+ part of the free fermionic field is shown to be causal and to not contain instantaneous terms. 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 factors are shown to be scalars and we find Z1 = Z3 at one loop order. The running coupling constant and QCD β function are also computed in the noncovariant light-cone gauge. Some comments on the relationship of our LF framework to the analytic effective charge and renormalization scheme defined by the pinch technique are made. LF quantization thus provides a consistent formulation of gauge theory, despite the fact that the hyperplanes x± = 0 used to impose boundary conditions constitute characteristic surfaces of a hyperbolic partial differential equation