The QCD Quark Propagator in Coulomb Gauge and - Institut für Physik

68 6.4. Electromagnetic current operator
Q
P
f
i
Ψ Ψ P
f
i
P
f
i
Ψ Ψ P
f
i
Q
P f
Γ − Γ
i
Ψ Ψ P
f
i
P
f
i
Ψ Ψ P
f
i
axial vector scalar
Q
Q
P Γ − µ
f
i
Ψ Ψ P
f
i
X
µ
Q
P
f
X−
Q
i
Ψ Ψ P
f
i
Γ
Figure 6.1: Nucleon-photon vertex which ensures a conserved current for on-shell nucleons
described by the Faddeev amplitudes, Ψ i,f , calculated in section6.3. The single line represents
S(p), the dressed-quark propagator, section6.3.2, and the double line, the diquark
propagator, section6.3.2; Γ is the diquark Bethe-Salpeter amplitude, section6.3.2; and the
remaining vertices are described in sections.6.4.1–6.4.5: the top-left image is diagram 1;
the top-right, diagram 2; and so on, with the bottom-right image, diagram 6.
as [cf. equation(6.48)]
〈 〉
P ′ |Ĵem µ |P
= Λ + (P ′ )
=
∫
d 4 p
(2π) 4
[
]
Pµ
BF
γ µ G E + M n (G
PBF
2 E − G M )
Λ + (P) (6.52)
d 4 k
(2π) 4 ¯Ψ(−p, P ′ )J em
µ (p, P ′ ; k, P)Ψ(k, P) . (6.53)
In figure6.1 we have broken the current, J em
µ (p, P ′ ; k, P), into a sum of six parts, each of
which we now make precise.