  We calculate the effect of a quadratic term in the energy dispersion on the
low-energy behavior of the Green's function of the spinless Tomonaga-Luttinger
model (TLM). Assuming that for small wave-vectors q = k - k_F the fermionic
excitation energy relative to the Fermi energy is v_F q + q^2 / (2m), we
explicitly calculate the single-particle Green's function for finite but small
values of lambda = q_c /(2k_F). Here k_F is the Fermi wave-vector, q_c is the
maximal momentum transfered by the interaction, and v_F = k_F / m is the Fermi
velocity. Assuming equal forward scattering couplings g_2 = g_4, we find that
the dominant effect of the quadratic term in the energy dispersion is a
renormalization of the anomalous dimension. In particular, at weak coupling the
anomalous dimension is tilde{gamma} = gamma (1 - 2 lambda^2 gamma), where gamma
is the anomalous dimension of the TLM. We also show how to treat the change of
the chemical potential due to the interactions within the functional
bosonization approach in arbitrary dimensions.
