Time-Dependent Perturbation Theory Studies of a Ground-State Many-Fermion System.

George Allen Baker Jr.

Colin John Lambert, W. E. Hagston

Employing an infinite hierarchy of equations for the Green functions of a many particle system in its ground state mod psi N ), the well known non-relativistic, time-dependent, ground-state perturbation theory of a normal system of interacting fermions is derived, without introducing the hypothesis that mod psi N ) is the adiabatic transform of a non-interacting state. This new formulation of the problem allows us to renormalise conventional perturbation theory by introducing an effective interaction Gamma and the final result is a highly summed and manifestly self-consistent perturbation expansion in powers of Gamma . The authors calculate Gamma to second order and demonstrate that many of the well known results of time-dependent perturbation theory may be obtained by choosing the simplest approximations for Gamma . The results are readily generalised to finite temperatures and the formalism provides a generalised form of Hartree-Fock theory which may have important applications in many areas of physics.

Robert William Jones, Franz Mohling, Richard L. Becker

Colin John Lambert

We examine in detail the microscopic theories of Beliaev and Hugenholtz and Pines as applied to an interacting system of bosons in its ground state and demonstrate that these theories are strictly applicable to a zero density gas only. After providing a re-normalization of the time dependent perturbation theory of a many fermion system in its ground state, we reformulate the corresponding boson theory without ab initio approximations concerning the k=0 mode.The resulting boson perturbation theory has a diagrammatic structure which is topologically identical with the corresponding fermion theory and provided the implicit assumptions concerning convergence are valid, we conclude that a finite fraction of the particles in an arbitrary interacting Bose gas at T=ok will not condense into the k=0 mode.

Robert William Jones, Franz Mohling

J. I. Hong