It has been recognized for some time that quantization on a null plane has several unique and remarkable advantages for the elucidation of quantum field theories. To date these unique features have not been exploited to solve strongly coupled, four-dimensional gauge theories. This is the first in a series of papers aimed at systematically formulating renormalizable gauge theories on the null plane. In order to lay down the groundwork for upcoming nonperturbative studies, it is indispensable to gain control over the perturbative treatment first. A discussion of one-loop renormalization of QED in the Hamiltonian formalism is presented. In this approach, one is faced with severe infrared divergences characteristic of the light-cone gauge. We show how to treat these divergences in a coherent fashion, and thus recover the usual results of the renormalization procedure such as Ward identities and coupling-constant renormalizations.

Field theories are regularized by discretization of the light-cone coordinates. As an example, the scalar-field quantization is carried out in detail, and the application to Monte Carlo computations is discussed.A rich amount of information on the nuclear structure has been gathered by means of deep-inelastic scattering of leptons off nuclear targets. These data, starting with the famous SLAC high-energy experiments of the later 1960s, and building up to the European Muon Collaboration (EMC) (among others), have established Q C D as the fundamental theory of the strong interactions. It has proved very convenient to analyze the results of these experiments in a null-plane frame, in particular when one studies such quantities as the structure functions, and Bjorken scaling: in this frame, one parametrizes the evolution in terms of x + rather than time x O , the associated "Hamiltonian" being Prather than PO. [Metric conventions:x e x = 2 x + x --x:.] Thus, the partons are viewed as carrying a fraction of p' ( p being the momentum of the target), and Bjorken's limit in the target rest frame corresponds simply to q--+w ( q being the momentum transfer).' Furthermore, light-cone coordinates offer an interesting system in which to construct field theories; for example, one finds then that the exact ground state is the bare Fock vacuum of the canonical quanta. The nullplane quantization of QCD, and its perturbative sector, is particularly elegant.2The agreement between theory and experiment (including scaling violations), no matter how impressive, has, however, been limited to the weak-coupling regime of QCD, where the property of asymptotic freedom can be exploited. Little has been achieved as yet in terms of deriving the full nonperturbative consequences of the model, in order to explain consistently even very basic data of nuclear physics such as confinement of color, mass ratios, etc., and make contact with the conceptual tools developed by the nuclear physicists.The most promising approach to the nonperturbative study of a field theory is provided by the lattice regularization, in conjunction with computational techniques: space-time is discretized, and physical quantities are expressed in the form of a path integral, because it is appropriate for a Monte Carlo c a l~u l a t i o n .~ A few qualitative features, such as the string picture of hadrons, have thus been satisfactorily reproduced.Some pioneering work has been done towards combining these theoretical methods by setting field theories on a light-cone lattice: Giles and Thorn discretized x + in a formulation which described interacting strings,4 while Bardeen, Pearson, and Rabinovici discretized the transverse coordinates x, (Ref. 5 ) . In this paper, we propose to discretize all four coordinates, with special attention devoted to x -. We hope by doing so to gain new insight into the physical aspects of a given theory such as the particle propagation, and also to be able in some cases to reduce the amount of computation required in comparison with a space-ti...

Massive Dirac fermions are canonically quantized on the null plane using the Dirac-Bergmann algorithm. The procedure is carried out in the framework of quantum electrodynamics as an illustration of a rigorous treatment of interacting fermion fields.

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