The quantum conductance of the single-electron tunneling (SET) transistor is investigated in this paper by the functional integral approach. The formalism is valid for arbitrary tunnel resistance of the junctions forming the SET transistor at any temperature. The path integrals are evaluated by the semiclassical method to yield an explicit non-perturbation form of the quantum conductance of the SET transistor. An anomaly of the quantum conductance is found if the tunnel resistances are much smaller than the quantum resistance. The dependence of the conductance on the gate voltage is also discussed.

4 pages including some mathe details of cond-mat/9908061