  We develop a theory of non-relativistic bosons in two spatial dimensions with
a weak short range attractive interaction. In the limit as the range of the
interaction becomes small, there is an ultra-violet divergence in the problem.
We devise a scheme to remove this divergence and produce a completely finite
formulation of the theory. This involves reformulating the dynamics in terms of
a new operator whose eigenvalues give the {\it logarithm} of the energy levels.
Then, a mean field theory is developed which allows us to describe the limit of
a large number of bosons. The ground state is a new kind of condensate
(soliton) of bosons that breaks translation invariance spontaneously. The
ground state energy is negative and its magnitude grows {\it exponentially}
with the number of particles, rather than like a power law as for conventional
many body systems.
