Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation.

中文翻译：

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费米气体中的玻色子集体激发

Hartree-Fock 理论已被证明是费米子系统的平均场近似。然而，它在预测物理性质方面存在一些缺陷，因此有必要建立量子相关性理论。最近，多体相关性的玻色子化已被严格证明是高密度下具有弱相互作用的相关能量的上限。我们回顾了玻色子近似，推导出了一个有效的哈密顿量。然后，我们表明，对于具有库仑相互作用的系统，该有效理论根据 Bohm 和 Pines 的随机相位近似以及实验观察来预测集体激发（等离子体）。