  Computing response functions by following the time evolution of
superoperators in Liouville space (whose vectors are ordinary Hilbert space
operators) offers an attractive alternative to the diagrammatic perturbative
expansion of many-body equilibrium and nonequilibrium Green functions. The
bookkeeping of time ordering is naturally maintained in real (physical) time,
allowing the formulation of Wick's theorem for superoperators, giving a
factorization of higher order response functions in terms of two fundamental
Green's functions. Backward propagations and the analytic continuations using
artificial times (Keldysh loops and Matsubara contours) are avoided. A
generating functional for nonlinear response functions unifies quantum field
theory and the classical mode coupling formalism of nonlinear hydrodynamics and
may be used for semiclassical expansions. Classical response functions may be
obtained without the explicit computation of stability matrices.
