Topologically distinct Feynman diagrams for mass operator in electron-phonon interaction

The new method for designing topologically distinct Feynman diagrams for electron's mass operator in electron-phonon interaction is developed using the permutation group theory. The carried out classification of DPs allows to choose the classes, corresponding to disconnected diagrams, to singly connected diagrams, direct ("tadpole") diagrams, to diagrams corresponding to phonon Green functions. After this classification the set of considered double permutations is reduced to one class since only these are relevant to mass operator. We derive analytical expressions which allow to identify the DP, and to choose the phonon components, which are not accepted in every type. To avoid repetition of asymmetric diagrams, which correspond to the same analytical expression, we introduce the procedure of inversion in phonon component, and identify symmetric as well as a pair of asymmetric phonon components. For every type of DP (denoted by its digital encoding), taking into account its symmetry, we perform a set of transformations on this DP, list all DPs of the type and all the corresponding Feynman diagrams of mass operator automatically. It is clear that no more expressions (diagrams) for the relevant order of perturbation theory for mass operator can be designed.