and where Λ $^{µ}$( p, p + q ), Σ( p ) and B ( p, p + q ) are the one-loop contributions. Thus, the ST identity for the vectorial vertex (50), in the tree approximation, becomes so that the validity of the ST identity requires that For the one-loop approximation, we have The diagrams representing these contributions are given by: (from now on, we restrict ourselves to the Feynman gauge, α = 1) with This contribution is entirely nonplanar and using / q = ( / q + / p − / l − m ) − ( / p − / l − m ) can be shown to satisfy where the nonplanar fermion self-energy is 12 S − 1 F ( p ) = [ Z$_{2}$ / p − m − δm − Σ( p ) ] , (73) Z$_{1}$$_{F}$ ˜ Z$_{3}$ / qe ip ∧ q = [ Z$_{2}$Z$_{5}$ ( / p + / q ) − ( m + δm ) Z$_{5}$ ] e ip ∧ q − [ Z$_{2}$Z$_{6}$ / p − ( m + δm ) Z$_{6}$ ] e ip ∧ $^{q}$, (74) Z$_{5}$ = Z$_{6}$ and ˜ Z$_{3}$/Z$_{5}$ = Z$_{2}$/Z$_{1}$$_{F}$ . (75) q$_{µ}$ Λ µ $_{a}$( p, p + q ) + q$_{µ}$ Λ µ $_{b}$( p, p + q ) + / qb ( q $^{2}$) = Σ( p ) − Σ( p + q ) + ( / p + / q − m ) B$_{1}$ ( p, p + q ) − B$_{2}$ ( p, p + q )( / p − m ) . (76) 1 . p q l GLYPH<c109> p-l p+q-l p+q GLYPH<c97> GLYPH<c98> = − ie Λ µ $_{a}$( p, p + q ) e ip ∧ q (77) = ∫ d $^{4}$l (2 π ) 4 − ig$_{αβ}$ l 2 ( − ieγ $^{α}$) iS$_{0}$ ( p + q − l )( − ieγ $^{µ}$) iS$_{0}$ ( p − l )( − ieγ $^{β}$) e − 2 il ∧ $^{q}$eip ∧ $^{q}$, iS$_{0}$ ( p ) = i / p − m . (78) q$_{µ}$ Λ µ $_{a}$( p, p + q ) = Σ$_{np}$( p ) − Σ$_{np}$( p + q ) , (79) − i Σ$_{np}$( p ) = ∫ d $^{4}$l (2 π ) 4 − ig$_{αβ}$ l 2 ( − ieγ $^{α}$) iS$_{0}$ ( p − l )( − ieγ $^{β}$) e − 2 il ∧ $^{q}$. (80)