Quantum chromodynamics and other field theories on the light cone

In recent years light-cone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground state of the full theory. 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 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. This 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 Hamiltonian formalism on the light cone.