Abstract
The variational Gaussian approximation is generalized to the time-dependent approach capable of giving time-dependent Green's functions. This covariant Gaussian approximation is represented, in full analogy with the classical approximation, as an initial truncation of the Dyson-Schwinger equations followed by functional differentiation of the effective action. Intuitively simple Schr\odinger and Heisenberg pictures of the approximation are also discussed.
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