Functional integral formulation of Brueckner-Hartree-Fock theory

A functional integral formalism is developed for the quantum many-fermion problem with a strong, short-range repulsive two-body potential. It is applied to nuclear transition amplitudes, for which the stationary phase approximation leads to a new time-dependent mean-field theory. The general equations of motion are non-local in time due to the dependence of the mean-field upon the initial and final states. For special choices of boundary conditions, these equations simplify to the well-known Brueckner-Hartree-Fock approximation or to its time-dependent generalization. A non-perturbative expression for the quantal corrections to the static Brueckner-Hartree-Fock mean-field is proposed using the example of the ground state energy.