These results will be discussed in the following Sections. A strictly theoretical physics point of view in this field was explored instead by CvitanoviД‡, Lautrup and Pearson, with conclusions identical to the ones of ArquГЁs and BГ©raud. A more physical approach was followed by Riddell and then by Brouder. A graphical approach was followed for instance by Kleinert, Pelster, Kastening and Bachmann. Here, we focus the attention on the combinatorial point of view studied in depth by Kucinskii and Sadovskii. The problem of counting Goldstone Diagrams has already been solved, Rossky and Karplus, but it is a rather difficult task to list all publications about Feynman diagrams counting. Mathematicians and physicists worked to combine theories of planar trees and rooted maps with the enumeration of Feynman diagrams for field theories, essentially quantum electrodynamics (QED), quantum gravity and quantum computing (Atiyah, Witten, tвЂ™Hooft, De Wolf, Di Francesco ). Important progress has been made in recent years in developing the interplay between theoretical physics and graph theory (Floer Fukaya, Schaeffer ). This paper took origin from his inquires on the subject and is dedicated to his memory. The problem of a correct and convenient counting of connected Feynman diagrams was often raised by Alfredo Molinari during his lectures in many-body physics.

Feynman diagram calculation tool