Path integrals and time-dependent mean-field theories

Abstract
We present a path integral formulation of the many-body problem, using a continuous and overcomplete set of vectors in the Hilbert space. The saddle-point approximation for the calculation of the functional integral leads to classical equation of motion which can be quantized in a well prescribed way. The time dependent Hartree-Fock equations are an example of such classical equations. They are obtained by integrating over an overcomplete set of Slater determinant

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