  We formulate a general approach for studying the low-frequency response of an
interacting quantum dot connected to leads in the presence of oscillating gate
voltages. The energy dissipated is characterized by the charge relaxation
resistance, which under the loose assumption of Fermi liquid behavior at low
energy, is shown to depend only on static charge susceptibilities. The
predictions of the scattering theory are recovered in the noninteracting limit
while the effect of interactions is simply to replace densities of states by
charge susceptibilities in formulas. In order to substantiate the Fermi liquid
picture in the case of a quantum RC geometry, we apply a renormalization group
analysis and derive the low-energy Hamiltonian for two specific models: the
Anderson and the Coulomb blockade models. The Anderson model is shown, using a
field theoretical approach based on Barnes slave bosons, to map onto the Kondo
model. We recover the well-known expression of the Kondo temperature for the
asymmetric Anderson model and compute the charge susceptibility. The Barnes
slave bosons are extended to the Coulomb blockade model where the
renormalization-group analysis can be carried out perturbatively up to zero
energy. All calculations agree with the Fermi liquid nature of the low-energy
fixed point and satisfy the Friedel sum rule.
