Correlation Functions Through Variational Methods

Abstract

A variational expression is constructed for generating functions in many-body theory, equilibrium and non-equilibrium statistical mechanics or field theory. Thermodynamic potentials, expectation values of observables, two-time and multi-time functions can be derived therefrom. Basic tools are the backward Heisenberg equation and a general method for building variational principles. The use of an independent-particle trial space leads for many-fermion systems not only to the static and dynamic Hartree-Fock approximations, but provides for the correlations and for the two-time functions expressions which involve the static and dynamic RPA kernels, which thus acquire a variational status. The approximation satisfies many consistency requirements.