I am trying to understand how to enumerate higher-order Feynman diagrams.
In his book on Elementary Particle Physics, Griffiths considers a simple "ABC toy theory" which has:
- three (scalar, massive) particles A, B, and C (which are their own antiparticles), and
- only one allowed interaction vertex ABC.
He counts explicitly the number of higher-order diagrams for the process $A+A\to B+B$ at order $g^4$, i.e. with 4 vertices.
What confuses me is that his result changes in the 2nd edition:
In the first edition of his book (p. 207) he finds that there are 15 because each additional line can start at one of the 5 lines of the original $A+A\to B+B$ diagram and end on the same or another line, so enumerating
- $1\to1$, $1\to2$, ..., $1\to5$,
- $2\to2$, ..., $2\to5$,
we end up with 15. $\Rightarrow$ This makes sense naively.
However, in the second, revised edition, he talks about 8 diagrams only (p. 217): 5 self-energy diagrams ($i\to i$, a line "sprouts a loop"), two vertex corrections ("a vertex becomes a triangle") and one box diagram.
My question: How many diagrams are there? 15 or 8? Where have the other 7 gone, e.g. a line connecting an initial and a final-state particle? Was it wrong to include them? If so why? Are they equivalent to another diagram or ruled out for some reason?