  We obtain for the attractive Dirac delta-function potential in
two-dimensional quantum mechanics a renormalized formulation that avoids
reference to a cutoff and running coupling constant. Dimensional transmutation
is carried out before attempting to solve the system, and leads to an
interesting eigenvalue problem in N-2 degrees of freedom (in the center of
momentum frame) when there are N particles. The effective Hamiltonian for N-2
particles has a nonlocal attractive interaction, and the Schrodinger equation
becomes an eigenvalue problem for the logarithm of this Hamiltonian. The 3-body
case is examined in detail, and in this case a variational estimate of the
ground-state energy is given.
