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The nonequilibrium tunnelling center model of a localized electronic levelcoupled to a fluctuating two-state system and to two electronic reservoirs, issolved via an Anderson-Yuval-Hamann mapping onto a plasma of alternatingpositive and negative charges time-ordered along the two "Keldysh" contoursneeded to describe nonequilibrium physics. The interaction between chargesdepends both on whether their time separation is small or large compared to adephasing scale defined in terms of the chemical potential difference betweenthe electronic reservoirs and on whether their time separation is larger orsmaller than a decoherence scale defined in terms of the current flowing fromone reservoir to another. A renormalization group transformation appropriate tothe nonequilibrium problem is defined. An important feature is the presence inthe model of a new coupling, essentially the decoherence rate, which acquiresan additive renormalization similar to that of the energy in equilibriumproblems. The method is used to study interplay between the dephasing-inducedformation of independent resonances tied to the two chemical potentials and thedecoherence which cuts off the scaling and leads to effectively classicallong-time behavior. We determine the effect of departures from equilibrium onthe localization-delocalization phase transition.

Coulomb Gas on the Keldysh Contour: Anderson-Yuval-Hamann representation of the Nonequilibrium Two Level System