  The spinless resonant level model is studied when it is coupled by hopping to
one of the arbitrary number of conduction electron channels. The Coulomb
interaction acts between the electron on the impurity and in the different
channels. In case of repulsive or attractive interaction the conduction
electrons are pushed away or attracted to ease or hinder the hopping by
creating unoccupied or occupied states, respectively. In the screening of the
hopping orthogonality catastrophe plays an important role. In equilibrium the
weak and strong coupling limit the renormalizations are treated by
perturbative, numerical and Anderson-Yuval Coulomb gas methods. In case of two
leads the current due to applied voltage is treated in the weak coupling limit.
The presented detailed study should help to test other methods suggested for
non-equilibrium transport.
