New approach to perturbation theory of many-particle systems

Lambert, Colin and Hagston, W. E. (1984) New approach to perturbation theory of many-particle systems. International Journal of Theoretical Physics, 23 (2). pp. 99-124. ISSN 0020-7748

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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.

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Journal Article
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International Journal of Theoretical Physics
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22 Oct 2012 10:38
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21 Nov 2022 22:50