physicsquantum field theoryrenormalizationcetztikz
This Feynman diagram corresponds to the integrand in this expression for ∂tΓk,a(1)(q)=−12∑i,jk,lN∫p1,p2p3′,p4′∂tRk,ij(p1,p2)Γk,jk(2)(p2,p3)+Rk,jk(p2,p3) Γk,akl(3)(q,p3,p4)Γk,li(2)(p4,p1)+Rk,li(p4,p1).\displaystyle \partial_t \Gamma_{k,a}^{(1)}(q) = -\frac{1}{2} \sum_{\substack{i,j\\k,l}}^N \int_{\substack{p_1,p_2\\p_3^\prime,p_4^\prime}} \frac{\partial_t R_{k,ij}(p_1,p_2)}{\Gamma_{k,jk}^{(2)}(p_2,p_3) + R_{k,jk}(p_2,p_3)} \, \frac{\Gamma_{k,akl}^{(3)}(q,p_3,p_4)}{\Gamma_{k,li}^{(2)}(p_4,p_1) + R_{k,li}(p_4,p_1)}.∂tΓk,a(1)(q)=−21i,jk,l∑N∫p1,p2p3′,p4′Γk,jk(2)(p2,p3)+Rk,jk(p2,p3)∂tRk,ij(p1,p2)Γk,li(2)(p4,p1)+Rk,li(p4,p1)Γk,akl(3)(q,p3,p4).
