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The graph with two vertices and $n > 1$ edges connecting them has been called the "banana graph" in a number of papers. For one example, see "Feynman Motives of Banana Graphs" by Aluffi and Marcoli, Comm. in Number Theory and Physics (2009) 1-57. (The short title of this paper is "Banana Motives", which I find endlessly entertaining.)

Does anyone know who coined the term "banana graph"?

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    $\begingroup$ Not an answer to the question : in my neck of the woods, this graph is usually called a dipole. I've never heard the term banana graph. (see also en.wikipedia.org/wiki/Dipole_graph) $\endgroup$
    – verret
    Commented Nov 7, 2012 at 18:25
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    $\begingroup$ I think the term comes from banana diagram, which seems to be used in physics since at least the first half of the 90's. Other names for the same diagram/graph seem to be basketball or sunset diagrams. The older papers are not accessible to me, so I don't know if an originator for the term is mentioned there. $\endgroup$
    – Jan Jitse Venselaar
    Commented Nov 7, 2012 at 20:45
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    $\begingroup$ actually, the sunset diagram is distinct from the banana diagram (see below) $\endgroup$
    – Carlo Beenakker
    Commented Nov 7, 2012 at 20:57

2 Answers 2

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banana diagram

These diagrams come by different names: "banana", "water melon", "basket ball". An early reference is M. Creutz - Feynman rules for lattice gauge theory, Rev. Mod. Phys. 50, 561–571 (1978). A more recent reference is S. Groote, J.G. Körner, A.A. Pivovarov - On the evaluation of sunset-type Feynman diagrams (1998).

There is a long tradition of giving fanciful names to Feynman diagrams. This is the sunset diagram:

sunset diagram
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I just had lunch with Oliver Schnetz and our conversation broached the topic whether any of us ever coined a name which stuck. He mentioned to be the first one to attach the word "banana" to the banana graph. As a witness serves his unpublished paper Calculation of the $\phi^4$ $6$-loop non-zeta transcendental from 1999 which deals with "$n$-banana diagrams". Later he suggested the term to Marcolli. She modified it to "banana graph" in her paper with Aluffi from 2009.

Incidentally, Oliver mentioned also that the name sunset diagram in Carlo's answer is a misnomer. It should be sunrise diagram because "the sun never sets on Quantum Field Theory" (D. Broadhurst) (-:

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    $\begingroup$ I'm not sure what to make of this answer - the "witness" that is being mentioned comes over 20 years after one of the references mentioned in the other answer. $\endgroup$
    – Wojowu
    Commented May 4, 2021 at 15:52

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