No 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.

Light-front ͑LF͒ quantization in the light-cone ͑LC͒ gauge is used to construct a renormalizable theory of the standard model. The framework derived earlier for QCD is extended to the Glashow-Weinberg-Salam ͑GWS͒ model of electroweak interaction theory. The Lorentz condition is automatically satisfied in LF-quantized QCD in the LC gauge for the free massless gauge field. In the GWS model, with the spontaneous symmetry breaking present, we find that the 't Hooft condition accompanies the LC gauge condition corresponding to the massive vector boson. The two transverse polarization vectors for the massive vector boson may be chosen to be the same as found in QCD. The nontransverse and linearly independent third polarization vector is found to be parallel to the gauge direction. The corresponding sum over polarizations in the standard model, indicated by K (k), has several simplifying properties similar to the polarization sum D (k) in QCD. The framework is unitary and ghost free ͑except for the ghosts at k ϩ ϭ0 associated with the light-cone gauge prescription͒. The massive gauge field propagator has well-behaved asymptotic behavior. The interaction Hamiltonian of electroweak theory can be expressed in a form resembling that of covariant theory, plus additional instantaneous interactions which can be treated systematically. The LF formulation also provides a transparent discussion of the Goldstone boson ͑or electroweak͒ equivalence theorem, as the illustrations show.