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Computing response functions by following the time evolution ofsuperoperators in Liouville space (whose vectors are ordinary Hilbert spaceoperators) offers an attractive alternative to the diagrammatic perturbativeexpansion of many-body equilibrium and nonequilibrium Green functions. Thebookkeeping of time ordering is naturally maintained in real (physical) time,allowing the formulation of Wick's theorem for superoperators, giving afactorization of higher order response functions in terms of two fundamentalGreen's functions. Backward propagations and the analytic continuations usingartificial times (Keldysh loops and Matsubara contours) are avoided. Agenerating functional for nonlinear response functions unifies quantum fieldtheory and the classical mode coupling formalism of nonlinear hydrodynamics andmay be used for semiclassical expansions. Classical response functions may beobtained without the explicit computation of stability matrices

Superoperator representation of nonlinear response: Unifying quantum field and mode coupling theories