  Quantum field theories require a cutoff to regulate divergences that result
from local interactions, and yet physical results can not depend on the value
of this cutoff. The renormalization group employs a transformation that changes
the cutoff to isolate hamiltonians that produce cutoff-independent eigenvalues.
The similarity renormalization group is based on similarity transformations
that regulate off-diagonal matrix elements, forcing the hamiltonian towards a
band-diagonal form as the cutoff is lowered. This avoids pathologies that
plagued tradition transformations acting on hamiltonians, making it possible to
produce a well-behaved perturbative approximation of renormalized hamiltonians
in asymptotically free theories. We employ a simple two-dimensional delta
function example to illustrate this new renormalization technique.
