Application of the Green’s functions method to the study of the optical properties of semiconductors

75 APPENDIX E. 77 APPENDIX F. 79 APPENDIX G. 82 APPENDIX H. Introduction. Generalized Green's functions. Equations of motion for the generalized single-particle Green's function. Bethe-Salpeter equation for the two-particle Green's function. Connection with linear-response theory. Conserving approximations. Gauge invariance, current conservation, and the Ward identities. Optical properties of semiconductors. Single-particle energy levels. Screening of static impurities. Excitonic states. A functional derivative identity. Dyson's equation. Reducible vs. irreducible parts of the correlation functions. Elimination of the spin variables and transformation to the energy-momentum representation. The Thomas-Reiche-Kuhn sum rule. The Clausius-Mossotti relation. The particle-hole Green's function. The Haken potential.

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