Quantum fields on the light front, formulation in coordinates close to the light front, lattice approximation$^1$

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 spacelike 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.