Pauli–Villars regularization and the light-front Hamiltonian in $(2+1)$-dimensional Yang–Mills theory

We consider the renormalization problem of the $(2{+}1)$-dimensional Yang–Mills theory quantized on the light front. We introduce extra fields analogous to those used in the Pauli–Villars regularization to restore the perturbative equivalence between the quantized theory and the conventional formulation in Lorentz coordinates. These fields realize an ultraviolet regularization of the theory. The obtained results allow constructing the renormalized Hamiltonian of the theory on the light front.