Coulomb Zero-Bias Anomaly: A Semiclassical Calculation

Effective action is proposed for the problem of Coulomb blocking of tunneling. The approach is well suited to deal with the ``strong coupling'' situation near zero bias, where perturbation theory diverges. By a semiclassical treatment, we reduce the physics to that of electrodynamics in imaginary time, and express the anomaly through exact conductivity of the system $\sigma(\omega, q)$ and exact interaction. For the diffusive anomaly, we compare the result with the perturbation theory of Altshuler, Aronov, and Lee. For the metal-insulator transition we derive exact relation of the anomaly and critical exponent of conductivity.