  The self-energy functional theory (SFT) is generalized to describe the
real-time dynamics of correlated lattice-fermion models far from thermal
equilibrium. This is achieved by means of a reformulation of the original
equilibrium theory in terms of double-time Green's functions on the
Keldysh-Matsubara contour. We construct a functional which is stationary at the
physical (nonequilibrium) self-energy and which yields the grand potential of
the initial thermal state at the physical point. Non-perturbative
approximations can be defined by specifying a reference system that serves to
generate trial self-energies. These self-energies are varied by varying the
reference system's one-particle parameters on the Keldysh-Matsubara contour. In
case of thermal equilibrium, the new approach reduces to the conventional SFT.
However, "unphysical" variations, i.e., variations that are different on the
upper and the lower branch of the Keldysh contour, must be considered to fix
the time-dependence of the optimal physical parameters via the variational
principle. Functional derivatives in the nonequilibrium SFT Euler equation are
carried out analytically to derive conditional equations for the variational
parameters that are accessible to a numerical evaluation via a time-propagation
scheme. Approximations constructed by means of the nonequilibrium SFT are shown
to be inherently causal, internally consistent and to respect macroscopic
conservation laws resulting from gauge symmetries of the Hamiltonian. This
comprises the nonequilibrium dynamical mean-field theory but also
dynamical-impurity and variational-cluster approximations that are specified by
reference systems with a finite number of degrees of freedom. In this way,
non-perturbative and consistent approximations can be set up, the numerical
evaluation of which is accessible to an exact-diagonalization approach.
