A Generalization of the Hartree Approximation and the Quantal Space-Time Correlation Function
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概要
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With use of Mori's continued-fraction method and making two approximations, (1) collisionless approximation and (2) the vertex part being dependent on the momentum transfer Q only, a generalized self-consistent Hartree-field equation and a set of self-consistent equations for the dynamic structure factor S(Q, ω), the self-energy Σ_p^R(ε) and the structure factor S(Q) are obtained for cases of Boson and Fermion systems. This generalized equation contains the self-energy effect through the effective interaction and the streaming term appearing in it. The moment sum rules for γ_Q(ω), the canonical autocorrelation of the density fluctuation, are investigated up to the fourth order. The second moment is given exactly both in the classical and zero self-energy limit. Our method yields an extension of Singwi and others' treatment of electron systems to include the self-energy effect and Mihara-Puff's integral equation for S(Q) of He^4 liquids. Dispersion relations of collective modes in the Boson, Fermion and classical fluids are given.
- 理論物理学刊行会の論文
- 1972-02-25
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