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Light front (LF) Hamiltonian for QED in (1 + 1) dimensions is constructed using the boson form of this model with additional Pauli–Villars-type ultraviolet regularization. Perturbation theory, generated by this LF Hamiltonian, is proved to be equivalent to usual covariant chiral perturbation theory. The obtained LF Hamiltonian depends explicitly on chiral condensate parameters which enter in a form of some renormalization of coupling constants. The obtained results can be useful when one attempts to apply LF Hamiltonian approach for (3 + 1) -dimensional models like QCD. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We briefly describe problems of the Hamiltonian approach for quantizing gauge fields on the light front for space–time bounded by the inequality |x-| ≤ L with periodic boundary conditions in the variable x- imposed on all fields (the DLCQ method). With these restrictions, we consider the gauge-invariant ultraviolet regularization by passing to a lattice in transverse coordinates. We remove the remaining ultraviolet divergences in the longitudinal momentum p- by imposing a gauge-invariant finite-mode regularization. It turns out that the canonical formalism on the light front with such a regularization imposed does not contain the usual most complicated second-class constraints between zero and nonzero modes of fields. The described scheme can be used both to regularize the standard gauge theory and to provide a gauge-invariant formulation of effective low-energy models on the light front. Because the manifest Lorentz invariance is broken in our formalism, the vacuum state is poorly defined. We discuss this problem, in particular, in relation to the problem of passing to the continuous space limit. [ABSTRACT FROM AUTHOR]