  We study the transport through a strongly interacting Anderson quantum dot at
zero-temperature using the real-time renormalization group (RT-RG) in the
framework of a kinetic equation for the reduced density operator. We further
develop the general finite temperature real-time transport formalism by
introducing field superoperators that obey fermionic statistics. This direct
second quantization in Liouville-Fock space strongly simplifies the
construction of operators and superoperators which transform irreducibly under
the Anderson-model symmetry transformations. The fermionic field superoperators
naturally arise from the univalence (fermion-parity) superselection rule for
the total system. Expressed in these field superoperators, the causal structure
of the perturbation theory for the effective time-evolution
superoperator-kernel becomes explicit. The causal structure also implies the
existence of a fermion-parity protected eigenvector of the exact Liouvillian,
explaining a recently reported result on adiabatic driving [Phys. Rev. B 85,
075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling.
Furthermore, in the WBL the causal representation exponentially reduces the
number of diagrams for the time-evolution kernel. We perform a complete 2-loop
RG analysis at finite voltage and magnetic field, while systematically
accounting for the dependence on both the quantum dot and reservoir
frequencies. Using the second quantization in Liouville-space and symmetry
restrictions we obtain analytical RT-RG equations with an efficient numerical
solution and we extensively study the model parameter space, excluding the
Kondo regime. The incorporated renormalization effects result in an enhancement
of the inelastic cotunneling peak. Moreover, we find a tunnel-induced
non-linearity of the stability diagrams at finite voltage, both in the SET and
ICT regime.
