  The one step fermionic ladder refers to two parallel Luttinger Liquids (poles
of the ladder) placed such that there is a finite probability of electrons
hopping between the two poles at a pair of opposing points along each of the
poles. The many-body Green function for such a system is calculated in presence
of forward scattering interactions using the powerful non-chiral bosonization
technique (NCBT). This technique is based on a non-standard harmonic analysis
of the rapidly varying parts of the density fields appropriate for the study of
strongly inhomogeneous ladder systems. The closed analytical expression for the
correlation function obtained from NCBT is nothing but the series involving the
RPA (Random Phase Approximation) diagrams in powers of the forward scattering
coupling strength resummed to include only the most singular terms with the
source of inhomogeneities treated exactly. Finally the correlation functions
are used to study physical phenomena such as Friedel oscillations and the
conductance of such systems with the potential difference applied across
various ends.
