  The absence of fermionic, asymptotical one-particle states in the Luttinger
model raises the suspicion that the interactions are actually strong at the
vicinity of the Fermi points. The functional internal space renormalization
group method, a systematical scheme for the computation of effective coupling
strengths off the Fermi points, is applied to shed some light on this issue. A
simple truncation of the evolution equation shows that the theory is indeed
strongly coupled at the Fermi points for arbitrarily small value of the bare
coupling constant and the removal of the cutoff is blocked by Landau poles. A
peculiar feature of the normal ordering scheme is pointed out to explain the
absence of these effects in the bosonized solution.
