Quantum fields on the light front, formulation in coordinates close to the light front, lattice approximation

We review the fundamental ideas of quantizing a theory on a light front including the Hamiltonian approach to the problem of bound states on the light front and the limiting transition from formulating a theory in Lorentzian coordinates (where the quantization occurs on space-like hyperplanes) to the theory on the light front, which demonstrates the equivalence of these variants of the theory. We describe attempts to find such a form of the limiting transition for gauge theories on the Wilson lattice. © 2006 Springer Science+Business Media, Inc.