14.2 Feynman Diagrams and Feynman Rules
301
(a)
(b)
(c)
Fig. 14.8 Factorization of the amplitude G 0,5 in channels and fundamental quintic vertex. Only
the cases where V 1 and V 2 factorize on one side are indicated, and the other cases follow
by permutations of the external states. (a) Factorization 12|3|45. (b) Factorization 12|345. (c)
Fundamental vertex
Tree-Level Quintic Vertex The amplitude A 0,5 can be factorized in a greater
number of channels, the two types being 2|2|1 and 2|3. The possible Feynman
graphs are built either from three cubic vertices and two propagators (Fig. 14.8a
and permutations) or from one cubic and one quartic vertices together with
one propagator (Fig. 14.8b and permutations). The remaining contribution is the
fundamental vertex (Fig. 14.8c):
V 0,5 (V 1 , . . . , V 5 ) :=
R 0,5
ω
0,5
4 (V 1 , . . . , V 5 ).
(14.55)
The construction to higher order follows exactly this scheme.