Diagram Expansion at Finite Temperatures in the Real Time and Frequency Domains

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Abstract
A method is given for obtaining diagram expansions at finite temperatures in domains for real times and frequencies. As an example the diagram expansions for electrons (in the ordinary electron gas approximation) and phonons are discussed. Network rules are established to obtain all kinds of self energies and propagators in a systematic and simple way. These specify the way in which the different types of propagators G, G≷, Gr. a for, e.g., electrons should be linked together. Generalized Dyson equations for the different electron and phonon propagators are given. As the results are significant both for non‐equilibrium and equilibrium phenomena the corresponding diagram expansions are discussed in terms of the space in which they are most easily handled namely ordinary space and Fourier space, respectively. A diagram dictionary including the network rules is also presented. Finally, the evaluation of screened diagrams is given as an example.

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