  The density density correlation function (most singular parts) of chiral
Luttinger liquids forming the fractional quantum Hall effect (FQHE) edge is
systematically derived in presence of a point-contact junction acting as a
localised scalar impurity and is shown to be expressible as compact analytical
functions with second order poles and involving the bare scale-independent
reflection and transmission coefficients. The results are validated on
comparison with standard fermionic perturbation theory. The linear response
Hall conductance in the absence of a point-contact is recovered from the
obtained density density correlation functions (DDCF). The system under
consideration is inhomogeneous with broken translational invariance and for
such systems in one dimension, the connected moments of the density fluctuation
operator beyond second order need not be included in order to retreive the most
singular parts of the correlations. The reason being that all odd moments of
the density are zero and all higher order even moments are less singular than
the quadratic moment. The implications of these results when used in
conjunction with bosonization methods in presence of impurity backscattering is
briefly discussed.
