E. FEYNMAN Diagrams

A diagram dictionary for electrons, which are FERMIons, and phonons, which are Bosons, are shown in Table E. Diagrams for electrons are in coordinate-time space, while phonon diagrams are in momentum-energy space. As described in Section 3.1.1, the GREEN's function can be interpreted as the creation of a particle at in space-time, the propagation of the corresponding perturbation to the point in space-time, where the particle is annihilated. Hence, the full GREEN's function is represented by a double line joining these two points. The free GREEN's function is characterized by a single line.

The COULOMB potential is represented by a wavy line with two inputs and outputs which can be coupled together to describe a self-interaction. The COULOMB interaction is assumed to be instantaneous. It is convenient to consider the inter-particle potential as a static instantaneous potential proportional to a delta function .

Intermediate variables describe events taking place between the two space-time arguments of the GREEN's function, but without any constraints for exact time or place. The overall amplitude involves an integration over these variables. Each time a FERMIon loop appears, the perturbation expression corresponding to this FEYNMAN diagram must be multiplied by a factor .

Electrons can also interact with phonons. For phonons it is more convenient to work in the momentum-energy rather than in the space-time domain. Diagrams concerning a free phonon GREEN's functions and the interaction between electrons and phonons are also shown in Table E. The factor refers to the electron-phonon interaction matrix elements.