Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Renormalised perturbation theory of normal systems
AU - Lambert, Colin
AU - Hagston, W. E.
PY - 1981/7
Y1 - 1981/7
N2 - 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.
AB - 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.
U2 - 10.1088/0305-4470/14/7/010
DO - 10.1088/0305-4470/14/7/010
M3 - Journal article
VL - 14
SP - 1533
EP - 1542
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
SN - 0305-4470
IS - 7
ER -