Gauge invariance Feynman diagrams

The a4 term requires evaluation of 891 four-loop Feynman diagrams. They fall naturally into five (gauge-invariant) groups according to the way closed electron loops (of vacuum-polarization (v-p) type and light-by-light (l-l) scattering... 

The next term A mij,/me) has contributions from 469 Feynman diagrams containing v-p loops and/or l-l scattering subdiagrams. They falls naturally into four (gauge invariant) groups according to the way closed electron or muon loops appear in them. 

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