  Several issues in the modal approach to quantum field theory are discussed.
Within the formalism of spherical field theory, differential renormalization is
presented and shown to result in a finite number of renormalization parameters.
Computations of the massless Thirring model in 1+1 dimensions are presented
using this approach.
  Diagonalization techniques in periodic field theory are demonstrated. Issues
of very large Hilbert spaces are considered and several approaches are
presented. The quasi sparse eigenvector (QSE) approach takes advantage of the
relatively small number of basis states that typically contribute significantly
to any particular eigenvector. Stochastic correction methods use Monte Carlo
calculations to calculate higher order corrections to the quasi sparse result.
  The quasi sparse eigenvector method and stochastic error correction are
applied to the Hubbard model. With U/t=4, the shift in the ground energy below
the U=0 value is found to within 1% for the 8x8 Hubbard model with 25/64
filling.
