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 - New approach to perturbation theory of many-particle systems
AU - Lambert, Colin
AU - Hagston, W. E.
PY - 1984/2
Y1 - 1984/2
N2 - We derive an infinite hierarchy of integral equations for the Green functions of a many-particle system. This set of equations forms the basis of a unified approach to the perturbation theory of many boson and many fermion systems and avoids the introduction of the adiabatic hypothesis. It is demonstrated how a well-known ground state perturbation theory of a system of interacting fermions is obtained without introducing disconnected diagrams. It is shown that the formalism allows a self-consistent determination of the condensate Green function of a condensed Bose system and a derivation of the Beliaev, Hugenholtz, and Pines result for the single-particle k 0 Green function is given. A new self-consistent equation for the k = 0 Green function is solved to yield the well-known self-energy relation 11 – 02 =which plays the role of a self-consistency condition on the theory.
AB - We derive an infinite hierarchy of integral equations for the Green functions of a many-particle system. This set of equations forms the basis of a unified approach to the perturbation theory of many boson and many fermion systems and avoids the introduction of the adiabatic hypothesis. It is demonstrated how a well-known ground state perturbation theory of a system of interacting fermions is obtained without introducing disconnected diagrams. It is shown that the formalism allows a self-consistent determination of the condensate Green function of a condensed Bose system and a derivation of the Beliaev, Hugenholtz, and Pines result for the single-particle k 0 Green function is given. A new self-consistent equation for the k = 0 Green function is solved to yield the well-known self-energy relation 11 – 02 =which plays the role of a self-consistency condition on the theory.
U2 - 10.1007/BF02080997
DO - 10.1007/BF02080997
M3 - Journal article
VL - 23
SP - 99
EP - 124
JO - International Journal of Theoretical Physics
JF - International Journal of Theoretical Physics
SN - 0020-7748
IS - 2
ER -