In this course we shall develop theoretical methods suitable for the description of the many-body phenomena, such as Hamiltonian second-quantized operator formalism, Greens functions, path integral, functional integral, and the quantum kinetic equation. The concepts to be introduced include, but are not limited to, the random phase approximation, the mean field theory (aka saddle-point, or semiclassical approximation), the tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integral, renormalization group..
譯文:在本課程中,我們將會建立適合描述多體現象的理論方法,例如漢米頓二次量子化算子形式、格林函數、路徑積分、函數積分和量子動力方程式等。這些方法主要涉及如隨機相近似、平均場論(aka 鞍點或半古典近似)、虛數時間中的隧道力學、瞬子、貝里相、 相干態路徑積分及重整化群等概念。
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