We address the problem of nonperturbative calculations on the light front in quantum field theory regularized by Pauli-Villars method. As a preliminary step we construct light front Hamiltonians in (2+1)-dimensional $\lambda\phi^4$ model, for the cases without and with spontaneous symmetry breaking. The renormalization of these Hamiltonians in Pauli-Villars regularization is carried out via comparison of all-order perturbation theory, generated by these Hamiltonians, and the corresponding covariant perturbation theory in Lorentz coordinates.Comment: LaTeX, 18 pages, 2 figures. Appendix B has been replaced. Some changes have been made in Introduction and Conclusion. The new list of references is more complete. Article will be published in International Journal of Theoretical Physics, the final publication is available at link.springer.co

In this paper we consider (2+1)-dimensional SU(N)-symmetric gauge theory within light front perturbation theory, regularized by the method analogous to Pauli-Villars regularization. This enables us to construct correct renormalized light front Hamiltonian.

The renormalization problem of (2+1)-dimensional Yang-Mills theory quantized on the light front is considered. Extra fields analogous to those used in Pauli-Villars regularization are introduced to restore perturbative equivalence between such quantized theory and conventional formulation in Lorentz coordinates. These fields also provide necessary ultraviolet regularization to the theory. Obtained results allow to construct renormalized Hamiltonian of the theory on the light front.

We present an attempt to construct a QCD Hamiltonian on the light front (LF), including a semiphenomenological description of vacuum effects. In this approach, we obtain the LF theory via a limit transition from the theory formulated on spacelike planes near the LF. For the zero Fourier modes of fields in the coordinate along the light cone to remain independent dynamical variables on the LF, we realize the limit transition differently for zero and nonzero modes. The zero modes then model the vacuum on the LF and allow introducing a semiphenomenological description of vacuum effects. For a gauge-invariant regularization, we introduce a lattice in the space of "transverse" coordinates and a gauge-invariant cutoff of the momentum component along the light cone. We introduce a new description of field variables on the lattice, using unitary matrices related to the lattice links for the gluon zero modes and Hermitian matrices related to the corresponding lattice sites for the nonzero modes.