多体問題とグリーン関数との関係の研究 : 高等量子力学における摂動理論(15)

概要

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In this paper, next subject is discussed. §36. Dyson's equation of boson. At first we consider all possible diagrams beginning and ending with just one boson line. We calculated modified propagators D'(q,ω) for all these possible sub-diagrams. Next we calculated the propagator D"(q,ω) corresponding to the sum of all sub-diagrams D'(q,ω) i.e. [numerical formula]. D"(q,ω) represents everything that can happen to a free boson in the crystal. Lastly we define another boson propagator [numerical formula] which contains only the propagators for connected diagrams and does not contain non-connected diagrams with fluctuations of the vacuum. Then the result in D"(q,ω) gives the product of D(q,ω) and S・matrix (1+V) for a vacuum diagram. The representation of D(q,ω) gives Dyson's equation of boson, say D(q,ω)=D_0+DΠD_0.
近畿大学の論文
2005-12-20