Contributions à l'Etude du Vertex Topologique en Théorie ... - Toubkal

L.B. Drissi et al. / Nuclear Physics B 801 [FS] (2008) 316–345 335Γ (2)−(q) = Γ(1)−(2)( (q)Γ − q2 )we can bring G 2 (q) into the formG 2 (q) =〈0|Γ + (1)Γ (1)−Then, comparing with(q)Γ(2)−G 3 =〈0|O 0 (x 0 )O 1 (x 1 )O 2 (x 2 )|0〉,(q2 ) |0〉.we get, in addition to Eqs. (6.11), the following:O 2 (x 2 ) = Γ +(2) (q2 ) .(6.13)(6.14)(6.15)(6.16)(3) G 3 (q) as a 4-point functionWe start from the expression of G 3 (q),G 3 (q) =〈0|Γ + (1)Γ −(3) (q)|0〉then use the identity,Γ (3)−(q) = Γ(2)−and substitute Γ (2)(3)( (q)Γ − q2 ) ,(6.17)(6.18)(q2 )) Γ (3) (q3 ) .(6.19)− (q) by Eq. (6.13), we get( 2∏Γ − (3) (1)(q) = Γ − (q) l=1Comparing withΓ (2)−−we obtainG 3 =〈0|O 0 (x 0 )O 1 (x 1 )O 2 (x 2 )O 3 (x 3 )|0〉,(6.20)O 0 (x 0 ) = Γ + (1),O 1 (x 1 ) = Γ −(1)( (q),2∏O 2 (x 2 ) = Γ (2) (− q2 )) ,l=1O 3 (x 3 ) = Γ −(3) (q3 ) .(6.21)(4) G 4 (q) as a 5-point functionStarting fromG 4 (q) =〈0|Γ + (1)Γ −(4) (q)|0〉then using the identities,Γ − (4) (3) (4)( (q) = Γ − (q)Γ − q2 ) ,Γ −(4) (q2 ) = Γ −(3) (q2 ) Γ −(4) (q3 ) ,Γ −(4) (q3 ) = Γ −(3) (q3 ) Γ −(4) (q4 ) ,(6.22)(6.23)