Light-cone quantization on the lattice

Deep-inelastic experiments find a more natural description in a null-plane frame than in space-time coordinates. With the motivation of calculating the structure functions non-perturbatively, the author proposes to regularize any field theory, and QCD in particular, by discretizing directly the light-cone coordinates. As an example, the quantization of the scalar field is carried out in detail. Starting from the classical field, he treats the constraints using the Dirac-Bergmann algorithm. He constructs explicitly the Fock space and the four-momentum operator. Aside from a species doubling, it is verified that the lattice propagator goes to its correct continuum limit. In order to compute the 'energy' spectrum, he establishes a path-integral formulation of matrix elements. The application to Monte-Carlo simulations is discussed. He reports on numerical results of the free theory in (1 + 1) dimensions