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I was reading some papers on the study of the optical properties of some metals and came upon these conference proceedings by Hopfield from 1972. They are on the study of the infrared properties of transition metals to better understand superconductivity. In them, I found these interesting "diagrams" followed by the discussion below.

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Fig.(1a) shows the "diagram" responsible for the electron-phonon coupling mass enhancement at the Fermi energy and for superconductivity. The process to be evaluated is the virtual process in which a phonon (wiggly line) is created with the simultaneous generation of an electron-hole pair, which later recombine and reabsorb the phonon. Two electron-phonon vertices are present in this process. The imaginary part of the dielectric constant (Fig. 1b) has to do with energy loss. The electron-phonon collision part of the energy loss is due to processes related to (1a) except that the electron or hole also interacts twice with the electromagnetic field, and the phonons could be either created or thermally present to begin with. This process is proportional to two electron-phonon vertices and two electron-photon interactions. Fortunately, the electron-photon interactions can be independently measured by studying the real part of the dielectric constant, which is understood in terms of the scattering of the photon off an electron as in (1c). Clearly dividing (1b) by (1c) produces a result in which the electron-photon interaction has disappeared and a measure of (la) can thus be obtained.

I know nothing of superconductivity, so I have no input about the discussion of diagram 1a. However, the discussions of diagrams 1b and 1c seem to be along the lines of the description of electromagnetic intraband absorption and light scattering using Fermi's Golden rule in second-order.

  1. My first question is: are these diagrams any rigorous tool, like the Feynman diagrams from quantum field theory, with a strict grammar and interpretation, or are they just illustrative pictures drawn by the author on the fly? I like the clear picture they provide of optical processes, and would even like to include them in my Master's thesis's discussion of optical processes.

  2. My other (tangentially related) question is: is it well-known that light-scattering by electrons is the quantum-mechanical mechanism behind the macroscopic real part of the electric susceptibility? If so, could anyone provide a reference where this is discussed? I have read Ridley's book Quantum processes in semiconductors and he describes the process of light-scattering using Fermi's Golden Rule in second-order but he never links it to the material's susceptilibity directly, as far as I can tell.

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