  We present a fermionic description of non-equilibrium multi-level systems.
Our approach uses the Keldysh path integral formalism and allows us to take
into account periodic drives, as well as dissipative channels. The technique is
based on the Majorana fermion representation of spin-1/2 models which follows
earlier applications in the context of spin and Kondo systems. We apply this
formalism to problems of increasing complexity: a dissipative two-level system,
a driven-dissipative multi-level atom, and a generalized Dicke model describing
many multi-level atoms coupled to a single cavity. We compare our theoretical
predictions with recent QED experiments and point out the features of a
counter-lasing transition. Our technique provides a convenient and powerful
framework for analyzing driven-dissipative quantum systems, complementary to
other approaches based on the solution of Lindblad master equations.
