  We study an attractive $\phi^4$ interaction using Tamm-Dancoff truncation
with light-front coordinates in $3+1$ dimensions. The truncated theory requires
a coupling constant renormalization, we compute its $\beta$ function
non-perturbatively, show that the model is asymptotically free, and find the
corresponding Callan-Symanzik equations. The model supports bound states, we
find the wave function for the ground state of the two-particle sector. We also
give a bound for the $N$-particle ground state energy within a mean field
approximation, including the corresponding result for the case of $2+1$
dimensions where the model does not require renormalization.
