  The density operator in the Luttinger model consists of two components, one
of which describes long-wave fluctuations and the other is related to the rapid
oscillations of the charge-density-wave (CDW) type, caused by short-range
electron correlations. It is commonly believed that the conductance is
determined by the long-wave component. The CDW component is considered only
when an impurity is present. We investigate the contribution of this component
to the dynamic density response of a Luttinger liquid free from impurities. We
show that the conventional form of the CDW density operator does not conserve
the number of particles in the system. We propose the corrected CDW density
operator devoid of this shortcoming and calculate the dissipative conductance
in the case when the one-dimensional conductor is locally disturbed by a
conducting probe. The contribution of the CDW component to conductance is found
to dominate over that of the long-wave component in the low-frequency regime.
