Pictures Paths Particles Processes

200 November 7, 2013
with the trivial auxilliary rules
= i¯h , = i . (7.101)
Q¯h
These rules are very similar to those we adopted in regular QED : however, in
general we have
≠ (7.102)
since the scalar-scalar-photon vertex still depends on the various momenta. We
now turn to the second vertex, with two photon lines. Not denoting the two
scalar propagators, we have
p
µ
k = 2i Q2
(p − q − k)sµ
q
¯h
(
= i Q¯h
)
(i¯h)
(i Q¯h )
(2q + k)µ −
(i Q¯h ) (
(2p − k)µ (i¯h) i Q¯h
)
,
(7.103)
in other words,
= − . (7.104)
The proof of current conservation again relies on the SDe’s for this model :
= + + ,
= + + ,
= + + ,
(7.105)
where again we have used semi-connected graphs. The handlebar operation is
now seen to lead to
= +
= −
+ −
(7.106)