  We extend the recently developed causal superfermion approach to the
real-time transport theory to time-dependent decay problems.Its usefulness is
illustrated for the Anderson model of a quantum dot with tunneling rates
depending on spin due to the ferromagnetic electrodes and/or spin polarization
of the tunnel junction. We set up a second quantization scheme for density
operators in the Liouville-Fock space constructing causal field superoperators
using the fundamental physical principles of causality/probability conservation
and the fermion-parity superselection (univalence). The time-dependent
perturbation series for the time-evolution is renormalized by explicitly
performing the wide-band limit on the superoperator level. The short and
long-time reservoir correlations are shown to be tightly linked to the
occurrence of causal field destruction and creation superoperators,
respectively. The effective theory takes as a reference a damped local system,
providing an interesting starting point for numerical calculations of memory
kernels in real-time. A remarkable feature of this approach is the natural
appearance of a measurable fermion-parity protected decay mode. It already can
be calculated exactly in the Markovian, infinite temperature limit by leading
order perturbation theory, yet persists unaltered for the finite temperature,
interaction and tunneling spin polarization. Furthermore, we show how a
Liouville-space analog of the Pauli principle directly leads to the exact
result in the noninteracting limit: surprisingly, it is obtained in finite
(second) order renormalized perturbation theory, both for the self-energy as
well as the time-evolution propagator. For this limit we calculate the
time-evolution of the full density operator starting from an arbitrary initial
state on the quantum dot, including spin and pairing coherences and
two-particle correlations.
