  Four-dimensional quantum field theories generally require regularization to
be well defined. This can be done in various ways, but here we focus on
Pauli--Villars (PV) regularization and apply it to nonperturbative calculations
of bound states. The philosophy is to introduce enough PV fields to the
Lagrangian to regulate the theory perturbatively, including preservation of
symmetries, and assume that this is sufficient for the nonperturbative case.
The numerical methods usually necessary for nonperturbative bound-state
problems are then applied to a finite theory that has the original symmetries.
The bound-state problem is formulated as a mass eigenvalue problem in terms of
the light-front Hamiltonian. Applications to quantum electrodynamics are
discussed.
