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14 Amplitude Factorization and Feynman Diagrams
not reproduce A 0,4 : the moduli space M 0,4 is not completely covered by the three
amplitudes. Equivalently, the projection of the section over P 0,4 does not cover all
of M 0,4 . The missing contribution is defined by the quartic vertex (Fig. 14.6)
V 0,4 (V 1 , V 2 , V 3 , V 4 ) :=
R 0,4
ω
0,4
2 (V 1 , . . . , V 4 ),
(14.53)
and the corresponding section is denoted by R 0,4 (Fig. 14.7). Denoting by F
(s,t,u)
0,4
the graphs 14.5 in the s-, t- and u-channels, one has the relation
A 0,4 = F
(s)
0,4 + F
(t)
0,4 + F
(u)
0,4 + V 0,4 .
(14.54)
Fig. 14.6 Fundamental quartic vertex
Fig. 14.7 A section S 0,4 over P 0,4 and the contribution from the s-, t- and u-channels (Fig. 14.5)
are indicated by the corresponding indices. The fundamental vertex is defined by the section V 0,4