The null-plane quantization is studied with the emphasis on the P+=O mode, by using Dirac's quantization for constrained systems. This mode is eliminated from the Hilbert space and the physical vacuum can be defined in a kinematical way. It enables us to con­ struct the physical Fock space kinematically. Poincare invariance is also studied in detail.

The Problem of P^+ = 0 Mode in the Null-Plane Field Theory and Dirac's Method of Quantization

Singularities of current commutators on the light cone

In these lectures we hope to provide an elementary introduction to selected topics in light-front dynamics. Starting from the study of free field theories of scalar boson, fermion, and massless vector boson, the canonical field commutators and propagators in the instant and front forms are compared and contrasted. Poincare algebra is described next where the explicit expressions for the Poincare generators of free scalar theory in terms of the field operators and Fock space operators are also given. Next, to illustrate the idea of Fock space description of bound states and to analyze some of the simple relativistic features of bound systems without getting into the wilderness of light-front renormalization, Quantum Electrodynamics in one space - one time dimensions is discussed along with the consideration of anomaly in this model. Lastly, light-front power counting is discussed. One of the consequences of light-front power counting in the simple setting of one space - one time dimensions is illustrated using massive Thirring model. Next, motivation for light-front power counting is discussed and power assignments for dynamical variables in three plus one dimensions are given. Simple examples of tree level Hamiltonians constructed by power counting are provided and finally the idea of reducing the number of free parameters in the theory by appealing to symmetries is illustrated using a tree level example in Yukawa theory.

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An Introduction to Light-Front Dynamics for Pedestrians

Light-Cone Commutator and High-Energy Lepton-Hadron Inelastic Scattering

We discuss the light-cone quantization of gauge theories from two perspectives: as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The light-cone Fock state expansion of wavefunctions at fixed light cone time provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of light-cone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavy-quark contributions to structure functions. A general non-perturbative method for numerically solving quantum field theories, “discretized light-cone quantization,” is outlined and applied to several gauge theories, including QCD in one space and one time dimension, and quantum electrodynamics in physical space-time at large coupling strength. The DLCQ method is invariant under the large class of light-cone Lorentz transformations, and it can be formulated such that ultraviolet regularization is independent of the momentum space discretization. Both the bound-state spectrum and the corresponding relativistic light-cone wavefunctions can be obtained by matrix diagonalization and related techniques. We also discuss the construction of the light-cone Fock basis, the structure of the light-cone vacuum, and outline the renormalization techniques required for solving gauge theories within the light-cone Hamiltonian formalism.

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Light-cone quantization of quantum chromodynamics

On the basis of observation that the fixed-mass sum rules are Fourier transforms of the commutators of currents on a lightlike hyperplane a new treatment of the algebra of currents is proposed. It consists in use of the currents integrated over the lightlike hyperplane (« lightlike » charges) and thus includes the commutators of currents on the whole light cone. An algebra of the lightlike charges is a sufficient assumption for the derivation of the fixed-mass sum rules and may be represented in the one-particle space with any momenta. Hence this extension of the usual equal-time current algebra allows us to abandon the methods likep→∞ without losing any of its advanteges.

J. Jersák

Papers

Algebra of currents on the light cone