(* ::Package:: *)

(* ::Input:: *)
(*(* The ultraviolet behavior of quantum gravity *)*)


(* ::Input:: *)
(*(* Absorbitive part of the graviton self-energy *)*)


(* ::Input:: *)
(*(** A - Definitions and general rules **)*)


(* ::Input:: *)
(*(*** A.1 - Definitions ***)*)


(* ::Input:: *)
(*Unprotect[Power,Times,Plus,Integer];*)
(*LamC=0;*)
(*lambda=1;*)
(*sigma=1;*)
(*SetAttributes[delta,Orderless]*)
(*SetAttributes[h,Orderless]*)
(*delta[mu_,nu_]^2:=4*)
(*delta[mu_,mu_]:=4*)
(*delta[mu_,nu_]A_[B___,mu_,Cc___]:=A[B,nu,Cc]*)
(*delta[mu_,nu_]A_[B___,mu_,Cc___][Dd___]:=A[B,nu,Cc][Dd]*)
(*delta[mu_,nu_]A_[B___][Dd___,mu_,Cc___]:=A[B][Dd,nu,Cc]*)
(*p[mu_]^2:=p2*)
(*q[mu_]^2:=q2*)
(*k[a_]^2:=k2*)
(*p[mu_]q[mu_]:=pq*)
(*p[a_]k[a_]:=pk*)
(*q[a_]k[a_]:=qk*)
(*kappa^m_:=0/;m>4*)
(*(a_+b_)[c_]:=a[c]+b[c]*)
(*(-a_)[b_]:=-a[b]*)
(*h[a_,b_][A___,c_,d_,B___]:=h[a,b][A,d,c,B]/;Sort[{c,d}]=!={c,d}*)
(*Der[h[a_,b_][A___],m_]:=h[a,b][A,m]*)
(*Der[A_+B_,m_]:=Der[A,m]+Der[B,m]*)
(*Der[A_ B_,m_]:=Der[A,m]B+A Der[B,m]*)
(*Der[A_^n_,m_]:=n Der[A,m]A^(n-1)*)
(*Der[A_,m_]:=0/;NumberQ[A]=!=False*)
(*Der[A_,m_]:=0/;A==kappa||A==Pi*)
(*Der[delta[m_,n_],r_]:=0*)
(*ginv[m_,n_,a_,b_]=ExpandAll[delta[m,n]-2 kappa h[m,n][]+4kappa^2 h[m,a][]h[a,n][]-8 kappa^3 h[m,a][]h[a,b][]h[b,n][]];*)


(* ::Input:: *)
(*sqrtg[a_,b_,c_]=ExpandAll[1+h[a,a][]kappa+((h[a,a][]h[b,b][])/2-h[a,b][]h[b,a][]) kappa^2+1/6 (h[a,a][]h[b,b][]h[c,c][]-6 h[a,a][] h[b,c][]h[c,b][]+8 h[a,b][]h[b,c][]h[c,a][]) kappa^3+1/24 (h[a,a][]h[b,b][]h[c,c][]h[d,d][]-12 h[a,a][]h[b,b][]  h[c,d][]h[d,c][]+12  h[a,b][]h[b,a][] h[c,d][]h[d,c][]+32 h[a,b][]h[b,c][]h[c,a][]h[d,d][]-48 h[a,b][]h[b,c][]h[c,d][]h[d,a][]) kappa^4];*)
(*Gammat[m_,n_,r_]=ExpandAll[kappa (h[n,r][m]+h[m,r][n]-h[m,n][r])];*)
(*Riem[m_,n_,r_,s_,a_,b_,c_,d_]=ExpandAll[kappa (h[m,s][n,r]-h[n,s][m,r]+h[n,r][m,s]-h[m,r][n,s])+ginv[a,b,c,d]Gammat[m,s,a]Gammat[n,r,b]-ginv[a,b,c,d]Gammat[m,r,a]Gammat[n,s,b]];*)
(*Ric[m_,n_,a_,b_,c_,d_,e_,f_,g_,i_]=ExpandAll[Riem[m,a,n,b,e,f,g,i]ginv[a,b,c,d]];*)
(*CDRic[m_,n_,t_,a_,b_,c_,d_,e1_,e2_,e3_,e4_,e5_,e6_,e7_,e8_]=ExpandAll[Der[Ric[m,n,e1,e2,e3,e4,e5,e6,e7,e8],t]-Gammat[m,t,a]ginv[a,b,c,d]Ric[b,n,e1,e2,e3,e4,e5,e6,e7,e8]-Gammat[n,t,a]ginv[a,b,c,d]Ric[m,b,e1,e2,e3,e4,e5,e6,e7,e8]];*)


(* ::Input:: *)
(*(*** A.2 - Symmetric integration rules ***)*)


(* ::Input:: *)
(*rul1=p[a_] :>0;*)
(*rul2=p[a_] p[b_] :>p2/4 delta[a,b];*)
(*rul3=p[a_] p[b_] p[c_]:>0;*)
(*delta4[a_,b_,c_,d_]=delta[a,b] delta[c,d]+delta[a,c] delta[b,d]+delta[a,d] delta[b,c];*)
(*rul4=p[a_] p[b_] p[c_] p[d_]:>p2^2/24 delta4[a,b,c,d];*)
(*rul5=p[a_] p[b_] p[c_] p[d_]p[e_]:>0;*)
(*delta6[a_,b_,c_,d_,e_,f_]=Expand[delta[a,b] delta4[c,d,e,f]+delta[a,c] delta4[b,d,e,f]+delta[a,d] delta4[c,b,e,f]+delta[a,e] delta4[c,d,b,f]+delta[a,f] delta4[c,d,e,b]];*)
(*rul6=p[a_] p[b_] p[c_] p[d_]p[e_]p[f_]:>p2^3/192 delta6[a,b,c,d,e,f];*)
(*rul7=p[a_] p[b_] p[c_] p[d_]p[e_]p[f_]p[g_]:>0;*)
(*delta8[a_,b_,c_,d_,e_,f_,g_,h_]=Expand[delta[a,b] delta6[c,d,e,f,g,h]+delta[a,c] delta6[b,d,e,f,g,h]+delta[a,d] delta6[c,b,e,f,g,h]+delta[a,e] delta6[c,d,b,f,g,h]+delta[a,f] delta6[c,d,e,b,g,h]+delta[a,g] delta6[c,d,e,f,b,h]+delta[a,h] delta6[c,d,e,f,g,b]];*)
(*rul8=p[a_] p[b_] p[c_] p[d_]p[e_]p[f_]p[g_]p[h_]:>p2^4/1920 delta8[a,b,c,d,e,f,g,h];*)
(*rul9=p[a_] p[b_] p[c_] p[d_]p[e_]p[f_]p[g_]p[h_]p[i_]:>0;*)
(*r44=pk^4 p[a_]p[b_]p[c_]p[d_]:>1/640 p2^4 (k2^2 delta[a,b] delta[c,d]+4 k2 delta[c,d] k[a] k[b]+4 k2 delta[b,d] k[a] k[c]+k2 delta[a,d] (k2 delta[b,c]+4 k[b] k[c])+4 k2 delta[b,c] k[a] k[d]+4 k2 delta[a,b] k[c] k[d]+8 k[a] k[b] k[c] k[d]+k2 delta[a,c] (k2 delta[b,d]+4 k[b] k[d]));*)
(*r43=pk^4 p[a_]p[b_]p[c_]:>0;*)
(*r42=pk^4 p[a_]p[b_]:>1/64 k2 p2^3 (k2 delta[a,b]+4 k[a] k[b]);*)
(*r41=pk^4 p[a_]:>0;*)
(*r40=pk^4:>(k2^2 p2^2)/8;*)
(*r34=pk^3 p[a_]p[b_]p[c_]p[d_]:>0;*)
(*r33=pk^3 p[a_]p[b_]p[c_]:>1/64 p2^3 (k2 delta[b,c] k[a]+k2 delta[a,c]k[b]+(k2 delta[a,b]+2 k[a]k[b]) k[c]);*)
(*r32=pk^3 p[a_]p[b_]:>0;*)
(*r31=pk^3 p[a_]:>1/8 k2 p2^2 k[a];*)
(*r30=pk^3:>0;*)
(*r24=pk^2 p[a_]p[b_]p[c_]p[d_]:>1/192 p2^3 (k2 delta[a,b] delta[c,d]+2 delta[c,d] k[a] k[b]+2 delta[b,d] k[a] k[c]+delta[a,d] (k2 delta[b,c]+2 k[b] k[c])+2 delta[b,c] k[a] k[d]+2 delta[a,b] k[c] k[d]+delta[a,c] (k2 delta[b,d]+2 k[b] k[d]));*)
(*r23=pk^2 p[a_]p[b_]p[c_]:>0;*)
(*r22=pk^2 p[a_]p[b_]:>1/24 p2^2 (k2 delta[a,b]+2 k[a] k[b]);*)
(*r21=pk^2 p[a_]:>0;*)
(*r20=pk^2:>(k2 p2)/4;*)
(*r14=pk p[a_]p[b_]p[c_]p[d_]:>0;*)
(*r13=pk p[a_]p[b_]p[c_]:>1/24 p2^2 (delta[b,c] k[a]+delta[a,c] k[b]+delta[a,b] k[c]);*)
(*r12=pk p[a_]p[b_]:>0;*)
(*r11=pk p[a_]:>1/4 p2 k[a];*)
(*r10=pk:>0;*)
(*r04=rul4;*)
(*r03=rul3;*)
(*r02=rul2;*)
(*r01=rul1;*)
(*rm4=pk^m_ p[a_]p[b_]p[c_]p[d_]:>1/(8 Gamma[4+m/2]) (1+(-1)^m) k2^(m/2) p2^(2+m/2) (1/Sqrt[\[Pi]] (delta[a,d] delta[b,c]+delta[a,c] delta[b,d]+delta[a,b] delta[c,d]) Gamma[(1+m)/2]+(2^(2-m) Gamma[1+m] k[a] k[b] k[c] k[d])/(k2^2 Gamma[-1+m/2])+1/(k2 Gamma[m/2]) 2^(1-m) Gamma[1+m] (delta[c,d] k[a] k[b]+delta[b,d] k[a] k[c]+delta[a,d] k[b] k[c]+delta[b,c] k[a] k[d]+delta[a,c] k[b] k[d]+delta[a,b] k[c] k[d]));*)
(*rm3=pk^m_ p[a_]p[b_]p[c_]:>-1/(4 Sqrt[\[Pi]] Gamma[(7+m)/2])(-1+(-1)^m) k2^(1/2 (-3+m)) p2^((3+m)/2) Gamma[1+m/2] (k2 delta[b,c] k[a]+k2 delta[a,c] k[b]+(k2 delta[a,b]+(-1+m) k[a] k[b]) k[c]);*)
(*rm2=pk^m_ p[a_]p[b_]:>((1+(-1)^m) k2^(-1+m/2) p2^(1+m/2) Gamma[(1+m)/2] (k2 delta[a,b]+m k[a] k[b]))/(4 Sqrt[\[Pi]] Gamma[3+m/2]);*)
(*rm1=pk^m_ p[a_]:>-((-1+(-1)^m) k2^(1/2 (-1+m)) p2^((1+m)/2) Gamma[1+m/2] k[a])/(2 Sqrt[\[Pi]] Gamma[(5+m)/2]);*)
(*rm0=pk^m_:>(p2 k2)^(m/2)((1+(-1)^m) Gamma[(1+m)/2])/(2 Sqrt[\[Pi]] Gamma[2+m/2]);*)
(*(* For the vertex *)*)
(*ru60=pk^6 p[m_]p[n_]:>1/128 k2^3 p2^4 delta[m,n]+3/64 k2^2 p2^4 k[m] k[n];*)
(*ru51=pk^5 pq p[m_]p[n_]:>1/128 k2^2 p2^4 qk delta[m,n]+1/32 k2 p2^4 qk k[m] k[n]+1/128 k2^2 p2^4 k[n] q[m]+1/128 k2^2 p2^4 k[m] q[n];*)
(*ru42=pk^4 pq^2 p[m_]p[n_]:>1/640 k2^2 p2^4 q2 delta[m,n]+1/160 k2 p2^4 qk^2 delta[m,n]+1/160 k2 p2^4 q2 k[m] k[n]+1/80 p2^4 qk^2 k[m] k[n]+1/80 k2 p2^4 qk k[n] q[m]+1/80 k2 p2^4 qk k[m] q[n]+1/320 k2^2 p2^4 q[m] q[n];*)
(*ru33=pk^3 pq^3 p[m_]p[n_]:>3/640 k2 p2^4 q2 qk delta[m,n]+1/320 p2^4 qk^3 delta[m,n]+3/320 p2^4 q2 qk k[m] k[n]+3/640 k2 p2^4 q2 k[n] q[m]+3/320 p2^4 qk^2 k[n] q[m]+3/640 k2 p2^4 q2 k[m] q[n]+3/320 p2^4 qk^2 k[m] q[n]+3/320 k2 p2^4 qk q[m] q[n];*)
(*ru24=pk^2 pq^4 p[m_]p[n_]:>1/640 k2 p2^4 q2^2 delta[m,n]+1/160 p2^4 q2 qk^2 delta[m,n]+1/320 p2^4 q2^2 k[m] k[n]+1/80 p2^4 q2 qk k[n] q[m]+1/80 p2^4 q2 qk k[m] q[n]+1/160 k2 p2^4 q2 q[m] q[n]+1/80 p2^4 qk^2 q[m] q[n];*)
(*ru15=pk pq^5 p[m_]p[n_]:>1/640 k2 p2^4 q2^2 delta[m,n]+1/160 p2^4 q2 qk^2 delta[m,n]+1/320 p2^4 q2^2 k[m] k[n]+1/80 p2^4 q2 qk k[n] q[m]+1/80 p2^4 q2 qk k[m] q[n]+1/160 k2 p2^4 q2 q[m] q[n]+1/80 p2^4 qk^2 q[m] q[n];*)
(*ru06=pq^6 p[m_]p[n_]:>1/128 p2^4 q2^3 delta[m,n]+3/64 p2^4 q2^2 q[m] q[n];*)
(*delta10[a_,b_,c_,d_,e_,f_,g_,h_,i_,l_]=Expand[delta[a,b] delta8[c,d,e,f,g,h,i,l]+delta[a,c] delta8[b,d,e,f,g,h,i,l]+delta[a,d] delta8[c,b,e,f,g,h,i,l]+delta[a,e] delta8[c,d,b,f,g,h,i,l]+delta[a,f] delta8[c,d,e,b,g,h,i,l]+delta[a,g] delta8[c,d,e,f,b,h,i,l]+delta[a,h] delta8[c,d,e,f,g,b,i,l]+delta[a,i] delta8[c,d,e,f,g,h,b,l]+delta[a,l] delta8[c,d,e,f,g,h,i,b]];*)
(*rul10=p[a_] p[b_] p[c_] p[d_]p[e_]p[f_]p[g_]p[h_]p[i_]p[l_]:>p2^5/23040 delta10[a,b,c,d,e,f,g,h,i,l];*)
(*rv80=pk^8 p[m_]p[n_]:>(7 k2^3 p2^5 (k2 delta[m,n]+8 k[m] k[n]))/1536;*)
(*rv71=pk^7 pq p[m_]p[n_]:>1/1536 7 k2^2 p2^5 (k2 qk delta[m,n]+k2 k[n] q[m]+k[m] (6 qk k[n]+k2 q[n]));*)
(*rv62=pk^6 pq^2 p[m_]p[n_]:>1/1536 k2 p2^5 (k2 (k2 q2+6 qk^2) delta[m,n]+2 (k2 q[m] (6 qk k[n]+k2 q[n])+3 k[m] (k2 q2 k[n]+4 qk^2 k[n]+2 k2 qk q[n])));*)
(*rv53=pk^5 pq^3 p[m_]p[n_]:>1/1536 p2^5 (k2 qk (3 k2 q2+4 qk^2) delta[m,n]+3 k2 q[m] ((k2 q2+4 qk^2) k[n]+2 k2 qk q[n])+k[m] (4 (3 k2 q2 qk+2 qk^3) k[n]+3 k2 (k2 q2+4 qk^2) q[n]));*)
(*rv44=pk^4 pq^4 p[m_]p[n_]:>1/7680 p2^5 ((3 k2^2 q2^2+24 k2 q2 qk^2+8 qk^4) delta[m,n]+4 (k[m] (3 q2 (k2 q2+4 qk^2) k[n]+4 qk (3 k2 q2+2 qk^2) q[n])+q[m] (4 (3 k2 q2 qk+2 qk^3) k[n]+3 k2 (k2 q2+4 qk^2) q[n])));*)
(*rv35=pk^3 pq^5 p[m_]p[n_]:>1/1536 p2^5 (q2 qk (3 k2 q2+4 qk^2) delta[m,n]+q[m] (3 q2 (k2 q2+4 qk^2) k[n]+4 qk (3 k2 q2+2 qk^2) q[n])+3 q2 k[m] (2 q2 qk k[n]+(k2 q2+4 qk^2) q[n]));*)
(*rv26=pk^2 pq^6 p[m_]p[n_]:>1/1536 p2^5 q2 (q2 (k2 q2+6 qk^2) delta[m,n]+2 (q2 k[m] (q2 k[n]+6 qk q[n])+3 q[m] (2 q2 qk k[n]+k2 q2 q[n]+4 qk^2 q[n])));*)
(*rv17=pk pq^7 p[m_]p[n_]:>1/1536 7 p2^5 q2^2 (q2 qk delta[m,n]+q2 k[n] q[m]+(q2 k[m]+6 qk q[m]) q[n]);*)
(*rv08=pq^8 p[m_]p[n_]:>(7 p2^5 q2^3 (q2 delta[m,n]+8 q[m] q[n]))/1536;*)
(*rw70=pk^7 p[m_]:>7/128 k2^3 p2^4 k[m];*)
(*rw61=pk^6 pq p[m_]:>1/128 k2^2 p2^4 (6 qk k[m]+k2 q[m]);*)
(*rw52=pk^5 pq^2 p[m_]:>1/128 k2 p2^4 ((k2 q2+4 qk^2) k[m]+2 k2 qk q[m]);*)
(*rw43=pk^4 pq^3 p[m_]:>1/640 p2^4 (4 (3 k2 q2 qk+2 qk^3) k[m]+3 k2 (k2 q2+4 qk^2) q[m]);*)
(*rw34=pk^3 pq^4 p[m_]:>1/640 p2^4 (3 q2 (k2 q2+4 qk^2) k[m]+4 qk (3 k2 q2+2 qk^2) q[m]);*)
(*rw25=pk^2 pq^5 p[m_]:>1/128 p2^4 q2 (2 q2 qk k[m]+(k2 q2+4 qk^2) q[m]);*)
(*rw16=pk pq^6 p[m_]:>1/128 p2^4 q2^2 (q2 k[m]+6 qk q[m]);*)
(*rw07=pq^7 p[m_]:>7/128 p2^4 q2^3 q[m];*)
(*rz80=pk^8:>(7 k2^4 p2^4)/128;*)
(*rz71=pk^7pq :>7/128 k2^3 p2^4 qk;*)
(*rz62=pk^6pq^2 :>1/128 k2^2 p2^4 (k2 q2+6 qk^2);*)
(*rz53=pk^5pq^3 :>1/128 k2 p2^4 qk (3 k2 q2+4 qk^2);*)
(*rz44=pk^4pq^4 :>1/640 p2^4 (3 k2^2 q2^2+24 k2 q2 qk^2+8 qk^4);*)
(*rz35=pk^3pq^5 :>1/128 p2^4 q2 qk (3 k2 q2+4 qk^2);*)
(*rz26=pk^2pq^6 :>1/128 p2^4 q2^2 (k2 q2+6 qk^2);*)
(*rz17=pk pq^7 :>7/128 p2^4 q2^3 qk;*)
(*rz08=pq^8 :>(7 p2^4 q2^4)/128;*)


(* ::Input:: *)
(*(*** A.3 - Lagrangian invariants ***)*)


(* ::Input:: *)
(*Ic=ExpandAll[sqrtg[vv1,vv2,vv3]];*)
(*Ic=Expand[2I kappa^2 Coefficient[Ic,kappa,2]];*)
(*Ic/.{A___ h[a_,b_][]:>A delta[a,zp]delta[b,wp],A___ h[a_,b_][m_]:>-I A p[m]delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_]:>- A p[m]p[n] delta[a,zp]delta[b,wp],h[a_,b_][]^2:>h[a,b][] delta[a,zp]delta[b,wp],h[a_,b_][m_]^2:>-I h[a,b][m] p[m]delta[a,zp]delta[b,wp],h[a_,b_][m_,n_]^2:>- h[a,b][m,n] p[m]p[n] delta[a,zp]delta[b,wp]};*)
(*%/.{h[a_,b_][]:>delta[a,zq]delta[b,wq],h[a_,b_][m_]:>-I q[m]delta[a,zq]delta[b,wq],h[a_,b_][m_,n_]:>- q[m]q[n] delta[a,zq]delta[b,wq]};*)
(*InvC0[zp_,wp_,zq_,wq_,p_,q_,p2_,q2_,pq_]=Expand[%];*)
(*InvCa[m_,n_,r_,s_,p_,p2_]=Expand[InvC0[m,n,r,s,p,-p,p2,p2,-p2]];*)
(*InvCb[m_,n_,r_,s_,p_,p2_]=Expand[1/2(InvCa[m,n,r,s,p,p2]+InvCa[n,m,r,s,p,p2])];*)
(*InvCc[m_,n_,r_,s_,p_,p2_]=Expand[1/2(InvCb[m,n,r,s,p,p2]+InvCb[m,n,s,r,p,p2])];*)
(*InvC[m_,n_,r_,s_,p_,p2_]=Expand[1/2(InvCc[m,n,r,s,p,p2]+InvCc[s,r,m,n,-p,p2])];*)
(*I0=ExpandAll[sqrtg[vv1,vv2,vv3]ginv[n,r,n2,n3]Ric[n,r,c1,c2,c3,c4,c5,c6,c7,c8]];*)
(*I0=Expand[2I kappa^2 Coefficient[I0,kappa,2]];*)
(*I0/.{A___ h[a_,b_][]:>A delta[a,zp]delta[b,wp],A___ h[a_,b_][m_]:>-I A p[m]delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_]:>- A p[m]p[n] delta[a,zp]delta[b,wp],h[a_,b_][]^2:>h[a,b][] delta[a,zp]delta[b,wp],h[a_,b_][m_]^2:>-I h[a,b][m] p[m]delta[a,zp]delta[b,wp],h[a_,b_][m_,n_]^2:>- h[a,b][m,n] p[m]p[n] delta[a,zp]delta[b,wp]};*)
(*%/.{h[a_,b_][]:>delta[a,zq]delta[b,wq],h[a_,b_][m_]:>-I q[m]delta[a,zq]delta[b,wq],h[a_,b_][m_,n_]:>- q[m]q[n] delta[a,zq]delta[b,wq]};*)
(*Inv0[zp_,wp_,zq_,wq_,p_,q_,p2_,q2_,pq_]=Expand[%];*)
(*Inv0a[m_,n_,r_,s_,p_,p2_]=Expand[Inv0[m,n,r,s,p,-p,p2,p2,-p2]];*)
(*Inv0b[m_,n_,r_,s_,p_,p2_]=Expand[1/2(Inv0a[m,n,r,s,p,p2]+Inv0a[n,m,r,s,p,p2])];*)
(*Inv0c[m_,n_,r_,s_,p_,p2_]=Expand[1/2(Inv0b[m,n,r,s,p,p2]+Inv0b[m,n,s,r,p,p2])];*)
(*InvR[m_,n_,r_,s_,p_,p2_]=Expand[1/2(Inv0c[m,n,r,s,p,p2]+Inv0c[s,r,m,n,-p,p2])];*)
(*I1=ExpandAll[sqrtg[vv1,vv2,vv3]ginv[m,n1,m2,m3]ginv[n,r,n2,n3]Ric[m,n,bp1,bp2,bp3,b4,b5,b6,b7,b8]Ric[n1,r,c1,c2,c3,c4,c5,c6,c7,c8]];*)
(*I1=Expand[2 I kappa^2Coefficient[I1,kappa,2]];*)
(*I1/.{A___ h[a_,b_][]:>A delta[a,zp]delta[b,wp],A___ h[a_,b_][m_]:>- I A p[m]delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_]:>- A p[m]p[n] delta[a,zp]delta[b,wp],h[a_,b_][]^2:>h[a,b][] delta[a,zp]delta[b,wp],h[a_,b_][m_]^2:>- I h[a,b][m] p[m]delta[a,zp]delta[b,wp],h[a_,b_][m_,n_]^2:>- h[a,b][m,n] p[m]p[n] delta[a,zp]delta[b,wp]};*)
(*%/.{h[a_,b_][]:>delta[a,zq]delta[b,wq],h[a_,b_][m_]:>- I q[m]delta[a,zq]delta[b,wq],h[a_,b_][m_,n_]:>- q[m]q[n] delta[a,zq]delta[b,wq]};*)
(*Inv1[zp_,wp_,zq_,wq_,p_,q_,p2_,q2_,pq_]=Expand[%];*)
(*Inv1a[m_,n_,r_,s_,p_,p2_]=Expand[Inv1[m,n,r,s,p,-p,p2,p2,-p2]];*)
(*Inv1b[m_,n_,r_,s_,p_,p2_]=Expand[1/2(Inv1a[m,n,r,s,p,p2]+Inv1a[n,m,r,s,p,p2])];*)
(*Inv1c[m_,n_,r_,s_,p_,p2_]=Expand[1/2(Inv1b[m,n,r,s,p,p2]+Inv1b[m,n,s,r,p,p2])];*)
(*InvRic2[m_,n_,r_,s_,p_,p2_]=Expand[1/2(Inv1c[m,n,r,s,p,p2]+Inv1c[s,r,m,n,-p,p2])];*)
(*I2=ExpandAll[sqrtg[vv1,vv2,vv3]ginv[m,n,m2,m3]ginv[n1,r,n2,n3]Ric[m,n,bp1,bp2,bp3,b4,b5,b6,b7,b8]Ric[n1,r,c1,c2,c3,c4,c5,c6,c7,c8]];*)
(*I2=Expand[2 I kappa^2Coefficient[I2,kappa,2]];*)
(*I2/.{A___ h[a_,b_][]:>A delta[a,zp]delta[b,wp],A___ h[a_,b_][m_]:>- I A p[m]delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_]:>- A p[m]p[n] delta[a,zp]delta[b,wp],h[a_,b_][]^2:>h[a,b][] delta[a,zp]delta[b,wp],h[a_,b_][m_]^2:>- I h[a,b][m] p[m]delta[a,zp]delta[b,wp],h[a_,b_][m_,n_]^2:>- h[a,b][m,n] p[m]p[n] delta[a,zp]delta[b,wp]};*)
(*%/.{h[a_,b_][]:>delta[a,zq]delta[b,wq],h[a_,b_][m_]:>- I q[m]delta[a,zq]delta[b,wq],h[a_,b_][m_,n_]:>- q[m]q[n] delta[a,zq]delta[b,wq]};*)
(*Inv2[zp_,wp_,zq_,wq_,p_,q_,p2_,q2_,pq_]=Expand[%];*)
(*Inv2a[m_,n_,r_,s_,p_,p2_]=Expand[Inv2[m,n,r,s,p,-p,p2,p2,-p2]];*)
(*Inv2b[m_,n_,r_,s_,p_,p2_]=Expand[1/2(Inv2a[m,n,r,s,p,p2]+Inv2a[n,m,r,s,p,p2])];*)
(*Inv2c[m_,n_,r_,s_,p_,p2_]=Expand[1/2(Inv2b[m,n,r,s,p,p2]+Inv2b[m,n,s,r,p,p2])];*)
(*InvR2[m_,n_,r_,s_,p_,p2_]=Expand[1/2(Inv2c[m,n,r,s,p,p2]+Inv2c[s,r,m,n,-p,p2])];*)


(* ::Input:: *)
(*(*** A.4 - Lagrangian ***)*)


(* ::Input:: *)
(*Lagra1kappa2=ExpandAll[-1/2 2 LamC sqrtg[a1,a2,a3]-zeta/2 sqrtg[a1,a2,a3] ginv[m,n,a4,a5]Ric[m,n,b1,b2,b3,b4,b5,b6,b7,b8]]+xi/12 sqrtg[vv1,vv2,vv3]ginv[m,n,m2,m3]ginv[n1,r,n2,n3]Ric[m,n,b1,b2,b3,b4,b5,b6,b7,b8]Ric[n1,r,c1,c2,c3,c4,c5,c6,c7,c8];*)


(* ::Input:: *)
(*Lagra2gkappa2=Expand[-alpha/2sqrtg[a1,a2,a3] ginv[m,r,a6,a7]ginv[n,s,a8,a9]*)
(*(Ric[m,n,b1,b2,b3,b4,b5,b6,b7,b8]Ric[r,s,c1,c2,c3,c4,c5,c6,c7,c8]-1/3Ric[m,r,b1,b2,b3,b4,b5,b6,b7,b8]Ric[n,s,c1,c2,c3,c4,c5,c6,c7,c8])];*)
(*Lagra2gkappa2=ExpandAll[Lagra2gkappa2];*)


(* ::Input:: *)
(*Lagra1=Expand[Lagra1kappa2/kappa^2];*)
(*Lagra2g=Expand[Lagra2gkappa2/kappa^2];*)


(* ::Input:: *)
(*(** B - Vertices and propagators **)*)


(* ::Input:: *)
(*(*** B.1 - Ghost propagator and vertices ***)*)


(* ::Input:: *)
(*pgh[m_,n_,p_,p2_]:=-I/p2(delta[m,n]-(1+1/(2 omega))p[m]p[n]/p2)*)
(*Lgh=Expand[-2 kappa (I (p[n]+k[n])Cbar[m]-(omega+1) delta[m,n]I (p[r]+k[r])Cbar[r])(-I p[m]h[s,n][]-I p[n] h[s,m][]-I k[s] h[m,n][])C[s] ];*)
(*Lgh/.{Cbar[m_]:>delta[m,a]};*)
(*%/.{C[m_]:>delta[m,b]};*)
(*%/.{A___ h[a_,b_][]:>A delta[a,zk]delta[b,wk],A___ h[a_,b_][m_]:>-I A k[m]delta[a,zk]delta[b,wk]};*)
(*V3gh1[a_,zk_,wk_,b_,k_,p_,k2_,p2_,pk_]=Expand[I %];*)
(*V3gh[a_,m_,n_,b_,k_,p_,k2_,p2_,pk_]=Expand[1/2(V3gh1[a,m,n,b,k,p,k2,p2,pk]+V3gh1[a,n,m,b,k,p,k2,p2,pk])];*)
(*(* In V3gh[a,m,n,b,k,p,k2,p2,pk], a is the index of the antighost leg, m and n are the indices of the graviton leg, b is the index of the ghost leg. Moreover, k is the incoming momentum of the graviton leg, p is the incoming momentum of the ghost leg *)*)


(* ::Input:: *)
(*(*** B.2 - Graviton propagator ***)*)


(* ::Input:: *)
(*Lgf=Expand[Lagra1+Lagra2g+ lamb (h[m,n][n]-(omega+1) h[n,n][m])(h[m,r][r]-(omega+1) h[r,r][m])];*)


(* ::Input:: *)
(*Q2=Coefficient[Lgf,kappa,0];*)
(*Q2=Q2/.{A___ h[a_,b_][]:>A delta[a,zp]delta[b,wp],A___ h[a_,b_][m_]:>-I A p[m]delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_]:>- A p[m]p[n] delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_,r_]:>I A p[m]p[n] p[r] delta[a,zp]delta[b,wp],h[a_,b_][]^2:>h[a,b][] delta[a,zp]delta[b,wp],h[a_,b_][m_]^2:>-I h[a,b][m] p[m]delta[a,zp]delta[b,wp],h[a_,b_][m_,n_]^2:>- h[a,b][m,n] p[m]p[n] delta[a,zp]delta[b,wp], h[a_,b_][m_,n_,r_]^2:>I h[a,b][m,n,r] p[m]p[n] p[r] delta[a,zp]delta[b,wp]};*)
(*Q2=Q2/.{h[a_,b_][]:>delta[a,zq]delta[b,wq],A___ h[a_,b_][m_]:>-I A q[m]delta[a,zq]delta[b,wq],h[a_,b_][m_,n_]:>- q[m]q[n] delta[a,zq]delta[b,wq],h[a_,b_][m_,n_,r_]:>I q[m]q[n] q[r] delta[a,zq]delta[b,wq]};*)
(*QQ[zp_,wp_,zq_,wq_,p_,q_,p2_,q2_,pq_]=Q2;*)
(*QQ2[m_,n_,r_,s_,p_,p2_]=QQ[m,n,r,s,p,-p,p2,p2,-p2];*)
(*QQ3[m_,n_,r_,s_,p_,p2_]=1/2(QQ2[m,n,r,s,p,p2]+QQ2[n,m,r,s,p,p2]);*)
(*QQ4[m_,n_,r_,s_,p_,p2_]=1/2(QQ3[m,n,r,s,p,p2]+QQ3[m,n,s,r,p,p2]);*)
(*Qu[m_,n_,r_,s_,p_,p2_]=Expand[QQ4[m,n,r,s,p,p2]+QQ4[r,s,m,n,-p,p2]];*)


(* ::Input:: *)
(*PP[r_,s_,m_,n_,p_,p2_]=aa (delta[m,s] delta[n,r]+delta[m,r] delta[n,s])+bb  delta[m,n] delta[r,s]+cc (delta[r,s] p[m] p[n]+ delta[m,n] p[r] p[s])+dd (delta[m,r] p[n] p[s]+ delta[m,s] p[n] p[r]+delta[n,r] p[m] p[s]+ delta[n,s] p[m] p[r])+ee p[m] p[n] p[r] p[s];*)
(*riss=Simplify[Expand[PP[m,n,a,b,p,p2]Qu[a,b,r,s,p,p2]]];*)
(*cc1=Simplify[Coefficient[riss,delta[m,n] delta[r,s]]];*)
(*cc2=Simplify[Coefficient[riss,delta[m,r] delta[n,s]]];*)
(*cc3=Simplify[Coefficient[riss,delta[m,r] p[n] p[s]]];*)
(*cc4=Simplify[Coefficient[riss,delta[m,n] p[r] p[s]]];*)
(*cc5=Simplify[Coefficient[riss,p[m] p[n] p[r] p[s]]];*)
(*sol=Simplify[Solve[{cc1==0,cc2==I/2,cc3==0,cc4==0,cc5==0},{aa,bb,cc,dd,ee}]];*)
(*sol=Simplify[Expand[sol]];*)
(*ppp=PP[m,n,r,s,p,p2]/.sol[[1]];*)
(*ppp=Simplify[ppp/.{lamb->lambda (sigma zeta-alpha p2)}];*)
(*ppp=Expand[ppp/.{alpha-> u alpha, xi-> u xi}];*)
(*ppp=Expand[Normal[Series[ppp,{u,0,2}]]/.{u->1}];*)
(*ppp=Expand[ppp/.{p2-> u p2}];*)
(*ppp=Expand[Normal[Series[ppp,{u,0,-1}]]/.{u->1}];*)
(*P[m_,n_,r_,s_,p_,p2_]=%;*)


(* ::Input:: *)
(*(*** B.3 - Graviton vertices ***)*)


(* ::Input:: *)
(*(**** B.1.a - Relevant portions of the Lagrangian ****)*)


(* ::Input:: *)
(*Lagra=Expand[Lagra1+Lagra2g];*)
(*Vert3=kappa Coefficient[Lagra,kappa,1];*)
(*Vert3=Expand[Vert3];*)


(* ::Input:: *)
(*(**** B.1.b - Three graviton vertex ****) *)


(* ::Input:: *)
(*Expand[Vert3/.{A___ h[a_,b_][]:>A delta[a,zp]delta[b,wp],A___ h[a_,b_][m_]:>-I A p[m]delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_]:>- A p[m]p[n] delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_,r_]:> I A p[m]p[n] p[r] delta[a,zp]delta[b,wp],A___ h[a_,b_][]^2:>A h[a,b][] delta[a,zp]delta[b,wp],A___ h[a_,b_][m_]^2:>-I A h[a,b][m] p[m]delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_]^2:>- A h[a,b][m,n] p[m]p[n] delta[a,zp]delta[b,wp], A___ h[a_,b_][m_,n_,r_]^2:> I A h[a,b][m,n,r] p[m]p[n] p[r] delta[a,zp]delta[b,wp]}];*)
(*Expand[%/.{A___ h[a_,b_][]:>A delta[a,zq]delta[b,wq],A___ h[a_,b_][m_]:>-I A q[m]delta[a,zq]delta[b,wq],A___ h[a_,b_][m_,n_]:>- A q[m]q[n] delta[a,zq]delta[b,wq],A___ h[a_,b_][m_,n_,r_]:> I A q[m]q[n] q[r] delta[a,zq]delta[b,wq],h[a_,b_][]^2:>h[a,b][] delta[a,zq]delta[b,wq],h[a_,b_][m_]^2:>-I h[a,b][m] q[m]delta[a,zq]delta[b,wq],h[a_,b_][m_,n_]^2:>- h[a,b][m,n] q[m]q[n] delta[a,zq]delta[b,wq], h[a_,b_][m_,n_,r_]^2:> I h[a,b][m,n,r] q[m]q[n] q[r] delta[a,zq]delta[b,wq]}];*)
(*Expand[%/.{h[a_,b_][]:>delta[a,z]delta[b,w],h[a_,b_][m_]:>I (p[m]+q[m])delta[a,z]delta[b,w],h[a_,b_][m_,n_]:>- (p[m]+q[m])(p[n]+q[n]) delta[a,z]delta[b,w],h[a_,b_][m_,n_,r_]:>-I (p[m]+q[m])(p[n]+q[n])(p[r]+ q[r]) delta[a,z]delta[b,w]}];*)


(* ::Input:: *)
(*V1[z_,w_,zp_,wp_,zq_,wq_,p_,q_,p2_,q2_,pq_]=ExpandAll[%];*)
(*V1a[z_,w_,zp_,wp_,zq_,wq_,p_,q_,p2_,q2_,pq_]=ExpandAll[I V1[z,w,zp,wp,zq,wq,p,q,p2,q2,pq]];*)
(*V2[z_,w_,m_,n_,r_,s_,p_,q_,p2_,q2_,pq_]=ExpandAll[1/2(V1a[z,w,m,n,r,s,p,q,p2,q2,pq]+V1a[w,z,m,n,r,s,p,q,p2,q2,pq])];*)
(*V3[z_,w_,m_,n_,r_,s_,p_,q_,p2_,q2_,pq_]=ExpandAll[1/2(V2[z,w,m,n,r,s,p,q,p2,q2,pq]+V2[z,w,n,m,r,s,p,q,p2,q2,pq])];*)
(*V4[z_,w_,m_,n_,r_,s_,p_,q_,p2_,q2_,pq_]=Expand[1/2(V3[z,w,m,n,r,s,p,q,p2,q2,pq]+V3[z,w,m,n,s,r,p,q,p2,q2,pq])];*)
(*V[z_,w_,m_,n_,r_,s_,p_,q_,p2_,q2_,pq_]=ExpandAll[V4[z,w,m,n,r,s,p,q,p2,q2,pq]+V4[m,n,z,w,r,s,-p-q,q,p2+q2+2 pq,q2,-pq -q2]+V4[r,s,m,n,z,w,p,-p-q,p2,p2+q2+2 pq,-p2-pq]+V4[z,w,r,s,m,n,q,p,q2,p2,pq]+V4[r,s,z,w,m,n,-p-q,p,p2+q2+2 pq,p2,-p2-pq]+V4[m,n,r,s,z,w,q,-p-q,q2,p2+q2+2 pq,-pq-q2]];*)
(*(* The three graviton vertex V[z,w,m,n,r,s,p,q,p2,q2,pq] has an external leg with indices m and n and incoming momentum p, an external leg with indices r and s and incoming momentum q, an external leg with indices z and w (and incoming momentum -p-q) *)*)


(* ::Input:: *)
(*(** C - Coefficients of the solution **)*)


(* ::Input:: *)
(*Deltaxi=5Ns/60;*)
(*Deltaalpha=-Ns/60;*)
(*a1=(alpha^5 k2^5)/(8640 \[Pi]^2 zeta^6)+(alpha^5 k2^5)/(61440 omega^4 \[Pi]^2 zeta^6)-(alpha^5 k2^5)/(11520 omega^2 \[Pi]^2 zeta^6)+(alpha^3 k2^5 xi^2)/(2160 \[Pi]^2 zeta^6)-(alpha^3 k2^5 xi^2)/(10240 omega^4 \[Pi]^2 zeta^6)-(alpha^3 k2^5 xi^2)/(3840 omega^3 \[Pi]^2 zeta^6)+(alpha^3 k2^5 xi^2)/(11520 omega^2 \[Pi]^2 zeta^6)+(alpha^3 k2^5 xi^2)/(1440 omega \[Pi]^2 zeta^6)+(alpha k2^5 xi^4)/(2160 \[Pi]^2 zeta^6)+(3 alpha k2^5 xi^4)/(20480 omega^4 \[Pi]^2 zeta^6)+(alpha k2^5 xi^4)/(1280 omega^3 \[Pi]^2 zeta^6)+(alpha k2^5 xi^4)/(640 omega^2 \[Pi]^2 zeta^6)+(alpha k2^5 xi^4)/(720 omega \[Pi]^2 zeta^6)-(11 alpha^4 k2^4)/(8640 \[Pi]^2 zeta^5)-(alpha^4 k2^4)/(4096 omega^4 \[Pi]^2 zeta^5)+(13 alpha^4 k2^4)/(11520 omega^2 \[Pi]^2 zeta^5)-(alpha^3 k2^4 xi)/(432 \[Pi]^2 zeta^5)+(7 alpha^3 k2^4 xi)/(10240 omega^4 \[Pi]^2 zeta^5)+(alpha^3 k2^4 xi)/(640 omega^3 \[Pi]^2 zeta^5)-(11 alpha^3 k2^4 xi)/(11520 omega^2 \[Pi]^2 zeta^5)-(alpha^3 k2^4 xi)/(240 omega \[Pi]^2 zeta^5)-(alpha^2 k2^4 xi^2)/(360 \[Pi]^2 zeta^5)+(alpha^2 k2^4 xi^2)/(1280 omega^4 \[Pi]^2 zeta^5)+(alpha^2 k2^4 xi^2)/(480 omega^3 \[Pi]^2 zeta^5)-(alpha^2 k2^4 xi^2)/(5760 omega^2 \[Pi]^2 zeta^5)-(alpha^2 k2^4 xi^2)/(240 omega \[Pi]^2 zeta^5)-(alpha k2^4 xi^3)/(216 \[Pi]^2 zeta^5)-(21 alpha k2^4 xi^3)/(10240 omega^4 \[Pi]^2 zeta^5)-(13 alpha k2^4 xi^3)/(1280 omega^3 \[Pi]^2 zeta^5)-(3 alpha k2^4 xi^3)/(160 omega^2 \[Pi]^2 zeta^5)-(11 alpha k2^4 xi^3)/(720 omega \[Pi]^2 zeta^5)-(k2^4 xi^4)/(2160 \[Pi]^2 zeta^5)-(3 k2^4 xi^4)/(20480 omega^4 \[Pi]^2 zeta^5)-(k2^4 xi^4)/(1280 omega^3 \[Pi]^2 zeta^5)-(k2^4 xi^4)/(640 omega^2 \[Pi]^2 zeta^5)-(k2^4 xi^4)/(720 omega \[Pi]^2 zeta^5)+(7 alpha^3 k2^3)/(4320 \[Pi]^2 zeta^4)-(19 alpha^3 k2^3)/(30720 omega^4 \[Pi]^2 zeta^4)-(alpha^3 k2^3)/(256 omega^3 \[Pi]^2 zeta^4)+(13 alpha^3 k2^3)/(11520 omega^2 \[Pi]^2 zeta^4)+(alpha^3 k2^3)/(96 omega \[Pi]^2 zeta^4)+(alpha^2 k2^3 xi)/(144 \[Pi]^2 zeta^4)-(39 alpha^2 k2^3 xi)/(10240 omega^4 \[Pi]^2 zeta^4)-(alpha^2 k2^3 xi)/(120 omega^3 \[Pi]^2 zeta^4)+(31 alpha^2 k2^3 xi)/(11520 omega^2 \[Pi]^2 zeta^4)+(7 alpha^2 k2^3 xi)/(480 omega \[Pi]^2 zeta^4)+(alpha k2^3 xi^2)/(180 \[Pi]^2 zeta^4)+(83 alpha k2^3 xi^2)/(10240 omega^4 \[Pi]^2 zeta^4)+(79 alpha k2^3 xi^2)/(1920 omega^3 \[Pi]^2 zeta^4)+(401 alpha k2^3 xi^2)/(5760 omega^2 \[Pi]^2 zeta^4)+(31 alpha k2^3 xi^2)/(720 omega \[Pi]^2 zeta^4)+(k2^3 xi^3)/(216 \[Pi]^2 zeta^4)+(21 k2^3 xi^3)/(10240 omega^4 \[Pi]^2 zeta^4)+(13 k2^3 xi^3)/(1280 omega^3 \[Pi]^2 zeta^4)+(3 k2^3 xi^3)/(160 omega^2 \[Pi]^2 zeta^4)+(11 k2^3 xi^3)/(720 omega \[Pi]^2 zeta^4)+(353 alpha^2 k2^2)/(8640 \[Pi]^2 zeta^3)+(17 alpha^2 k2^2)/(3840 omega^4 \[Pi]^2 zeta^3)+(39 alpha^2 k2^2)/(2560 omega^3 \[Pi]^2 zeta^3)-(5 alpha^2 k2^2)/(768 omega^2 \[Pi]^2 zeta^3)-(67 alpha^2 k2^2)/(2880 omega \[Pi]^2 zeta^3)+(43 alpha k2^2 xi)/(432 \[Pi]^2 zeta^3)-(39 alpha k2^2 xi)/(5120 omega^4 \[Pi]^2 zeta^3)-(53 alpha k2^2 xi)/(1280 omega^3 \[Pi]^2 zeta^3)-(35 alpha k2^2 xi)/(768 omega^2 \[Pi]^2 zeta^3)+(5 alpha k2^2 xi)/(72 omega \[Pi]^2 zeta^3)-(49 k2^2 xi^2)/(2160 \[Pi]^2 zeta^3)-(9 k2^2 xi^2)/(1024 omega^4 \[Pi]^2 zeta^3)-(127 k2^2 xi^2)/(2560 omega^3 \[Pi]^2 zeta^3)-(377 k2^2 xi^2)/(3840 omega^2 \[Pi]^2 zeta^3)-(29 k2^2 xi^2)/(360 omega \[Pi]^2 zeta^3)-(79 alpha k2)/(360 \[Pi]^2 zeta^2)-(alpha k2)/(1024 omega^4 \[Pi]^2 zeta^2)-(5 alpha k2)/(768 omega^3 \[Pi]^2 zeta^2)-(169 alpha k2)/(11520 omega^2 \[Pi]^2 zeta^2)-(19 alpha k2)/(160 omega \[Pi]^2 zeta^2)-(5 k2 xi)/(144 \[Pi]^2 zeta^2)+(11 k2 xi)/(1024 omega^4 \[Pi]^2 zeta^2)+(55 k2 xi)/(768 omega^3 \[Pi]^2 zeta^2)+(1537 k2 xi)/(11520 omega^2 \[Pi]^2 zeta^2)+(k2 xi)/(20 omega \[Pi]^2 zeta^2)-1/(30 \[Pi]^2 zeta)-1/(384 omega^4 \[Pi]^2 zeta)-7/(256 omega^3 \[Pi]^2 zeta)-25/(384 omega^2 \[Pi]^2 zeta)+1/(192 omega \[Pi]^2 zeta);*)
(*a2=-(alpha^5 k2^5)/(12960 \[Pi]^2 zeta^6)-(alpha^5 k2^5)/(92160 omega^4 \[Pi]^2 zeta^6)+(alpha^5 k2^5)/(17280 omega^2 \[Pi]^2 zeta^6)-(alpha^4 k2^5 xi)/(2592 \[Pi]^2 zeta^6)-(alpha^4 k2^5 xi)/(18432 omega^4 \[Pi]^2 zeta^6)+(alpha^4 k2^5 xi)/(3456 omega^2 \[Pi]^2 zeta^6)-(alpha^3 k2^5 xi^2)/(3240 \[Pi]^2 zeta^6)+(alpha^3 k2^5 xi^2)/(15360 omega^4 \[Pi]^2 zeta^6)+(alpha^3 k2^5 xi^2)/(5760 omega^3 \[Pi]^2 zeta^6)-(alpha^3 k2^5 xi^2)/(17280 omega^2 \[Pi]^2 zeta^6)-(alpha^3 k2^5 xi^2)/(2160 omega \[Pi]^2 zeta^6)-(alpha^2 k2^5 xi^3)/(648 \[Pi]^2 zeta^6)+(alpha^2 k2^5 xi^3)/(3072 omega^4 \[Pi]^2 zeta^6)+(alpha^2 k2^5 xi^3)/(1152 omega^3 \[Pi]^2 zeta^6)-(alpha^2 k2^5 xi^3)/(3456 omega^2 \[Pi]^2 zeta^6)-(alpha^2 k2^5 xi^3)/(432 omega \[Pi]^2 zeta^6)-(alpha k2^5 xi^4)/(3240 \[Pi]^2 zeta^6)-(alpha k2^5 xi^4)/(10240 omega^4 \[Pi]^2 zeta^6)-(alpha k2^5 xi^4)/(1920 omega^3 \[Pi]^2 zeta^6)-(alpha k2^5 xi^4)/(960 omega^2 \[Pi]^2 zeta^6)-(alpha k2^5 xi^4)/(1080 omega \[Pi]^2 zeta^6)-(k2^5 xi^5)/(648 \[Pi]^2 zeta^6)-(k2^5 xi^5)/(2048 omega^4 \[Pi]^2 zeta^6)-(k2^5 xi^5)/(384 omega^3 \[Pi]^2 zeta^6)-(k2^5 xi^5)/(192 omega^2 \[Pi]^2 zeta^6)-(k2^5 xi^5)/(216 omega \[Pi]^2 zeta^6)+(alpha^4 k2^4)/(810 \[Pi]^2 zeta^5)+(alpha^4 k2^4)/(4608 omega^4 \[Pi]^2 zeta^5)-(alpha^4 k2^4)/(960 omega^2 \[Pi]^2 zeta^5)+(13 alpha^3 k2^4 xi)/(1296 \[Pi]^2 zeta^5)+(7 alpha^3 k2^4 xi)/(23040 omega^4 \[Pi]^2 zeta^5)-(alpha^3 k2^4 xi)/(960 omega^3 \[Pi]^2 zeta^5)-(79 alpha^3 k2^4 xi)/(17280 omega^2 \[Pi]^2 zeta^5)+(alpha^3 k2^4 xi)/(360 omega \[Pi]^2 zeta^5)+(11 alpha^2 k2^4 xi^2)/(540 \[Pi]^2 zeta^5)-(alpha^2 k2^4 xi^2)/(320 omega^4 \[Pi]^2 zeta^5)-(29 alpha^2 k2^4 xi^2)/(2880 omega^3 \[Pi]^2 zeta^5)+(alpha^2 k2^4 xi^2)/(8640 omega^2 \[Pi]^2 zeta^5)+(7 alpha^2 k2^4 xi^2)/(270 omega \[Pi]^2 zeta^5)+(13 alpha k2^4 xi^3)/(648 \[Pi]^2 zeta^5)-(7 alpha k2^4 xi^3)/(7680 omega^4 \[Pi]^2 zeta^5)+(alpha k2^4 xi^3)/(1440 omega^3 \[Pi]^2 zeta^5)+(311 alpha k2^4 xi^3)/(17280 omega^2 \[Pi]^2 zeta^5)+(77 alpha k2^4 xi^3)/(2160 omega \[Pi]^2 zeta^5)+(29 k2^4 xi^4)/(810 \[Pi]^2 zeta^5)+(19 k2^4 xi^4)/(2560 omega^4 \[Pi]^2 zeta^5)+(43 k2^4 xi^4)/(960 omega^3 \[Pi]^2 zeta^5)+(k2^4 xi^4)/(10 omega^2 \[Pi]^2 zeta^5)+(53 k2^4 xi^4)/(540 omega \[Pi]^2 zeta^5)-(31 alpha^3 k2^3)/(3240 \[Pi]^2 zeta^4)-(alpha^3 k2^3)/(2880 omega^4 \[Pi]^2 zeta^4)+(alpha^3 k2^3)/(384 omega^3 \[Pi]^2 zeta^4)+(77 alpha^3 k2^3)/(17280 omega^2 \[Pi]^2 zeta^4)-(alpha^3 k2^3)/(144 omega \[Pi]^2 zeta^4)-(127 alpha^2 k2^3 xi)/(864 \[Pi]^2 zeta^4)+(11 alpha^2 k2^3 xi)/(1440 omega^4 \[Pi]^2 zeta^4)+(227 alpha^2 k2^3 xi)/(5760 omega^3 \[Pi]^2 zeta^4)+(629 alpha^2 k2^3 xi)/(17280 omega^2 \[Pi]^2 zeta^4)-(alpha^2 k2^3 xi)/(10 omega \[Pi]^2 zeta^4)-(77 alpha k2^3 xi^2)/(540 \[Pi]^2 zeta^4)+(7 alpha k2^3 xi^2)/(960 omega^4 \[Pi]^2 zeta^4)+(41 alpha k2^3 xi^2)/(2880 omega^3 \[Pi]^2 zeta^4)-(1147 alpha k2^3 xi^2)/(17280 omega^2 \[Pi]^2 zeta^4)-(293 alpha k2^3 xi^2)/(1440 omega \[Pi]^2 zeta^4)-(113 k2^3 xi^3)/(324 \[Pi]^2 zeta^4)-(3 k2^3 xi^3)/(80 omega^4 \[Pi]^2 zeta^4)-(259 k2^3 xi^3)/(960 omega^3 \[Pi]^2 zeta^4)-(229 k2^3 xi^3)/(320 omega^2 \[Pi]^2 zeta^4)-(33 k2^3 xi^3)/(40 omega \[Pi]^2 zeta^4)+(379 alpha^2 k2^2)/(4320 \[Pi]^2 zeta^3)-(133 alpha^2 k2^2)/(23040 omega^4 \[Pi]^2 zeta^3)-(809 alpha^2 k2^2)/(23040 omega^3 \[Pi]^2 zeta^3)-(205 alpha^2 k2^2)/(6912 omega^2 \[Pi]^2 zeta^3)+(709 alpha^2 k2^2)/(8640 omega \[Pi]^2 zeta^3)+(23 alpha k2^2 xi)/(54 \[Pi]^2 zeta^3)-(199 alpha k2^2 xi)/(11520 omega^4 \[Pi]^2 zeta^3)-(431 alpha k2^2 xi)/(5760 omega^3 \[Pi]^2 zeta^3)+(23 alpha k2^2 xi)/(1728 omega^2 \[Pi]^2 zeta^3)+(325 alpha k2^2 xi)/(864 omega \[Pi]^2 zeta^3)+(2261 k2^2 xi^2)/(2160 \[Pi]^2 zeta^3)+(109 k2^2 xi^2)/(1536 omega^4 \[Pi]^2 zeta^3)+(13207 k2^2 xi^2)/(23040 omega^3 \[Pi]^2 zeta^3)+(57787 k2^2 xi^2)/(34560 omega^2 \[Pi]^2 zeta^3)+(9347 k2^2 xi^2)/(4320 omega \[Pi]^2 zeta^3)-(271 alpha k2)/(1440 \[Pi]^2 zeta^2)+(29 alpha k2)/(2304 omega^4 \[Pi]^2 zeta^2)+(19 alpha k2)/(288 omega^3 \[Pi]^2 zeta^2)+(163 alpha k2)/(5760 omega^2 \[Pi]^2 zeta^2)-(271 alpha k2)/(1440 omega \[Pi]^2 zeta^2)-(149 k2 xi)/(144 \[Pi]^2 zeta^2)-(119 k2 xi)/(2304 omega^4 \[Pi]^2 zeta^2)-(65 k2 xi)/(144 omega^3 \[Pi]^2 zeta^2)-(7819 k2 xi)/(5760 omega^2 \[Pi]^2 zeta^2)-(4951 k2 xi)/(2880 omega \[Pi]^2 zeta^2)+29/(80 \[Pi]^2 zeta)+1/(96 omega^4 \[Pi]^2 zeta)+25/(256 omega^3 \[Pi]^2 zeta)+55/(192 omega^2 \[Pi]^2 zeta)+23/(64 omega \[Pi]^2 zeta);*)
(*a3=(alpha^5 k2^5)/(12960 \[Pi]^2 zeta^6)+(alpha^5 k2^5)/(92160 omega^4 \[Pi]^2 zeta^6)-(alpha^5 k2^5)/(17280 omega^2 \[Pi]^2 zeta^6)+(alpha^4 k2^5 xi)/(2592 \[Pi]^2 zeta^6)+(alpha^4 k2^5 xi)/(18432 omega^4 \[Pi]^2 zeta^6)-(alpha^4 k2^5 xi)/(3456 omega^2 \[Pi]^2 zeta^6)+(alpha^3 k2^5 xi^2)/(3240 \[Pi]^2 zeta^6)-(alpha^3 k2^5 xi^2)/(15360 omega^4 \[Pi]^2 zeta^6)-(alpha^3 k2^5 xi^2)/(5760 omega^3 \[Pi]^2 zeta^6)+(alpha^3 k2^5 xi^2)/(17280 omega^2 \[Pi]^2 zeta^6)+(alpha^3 k2^5 xi^2)/(2160 omega \[Pi]^2 zeta^6)+(alpha^2 k2^5 xi^3)/(648 \[Pi]^2 zeta^6)-(alpha^2 k2^5 xi^3)/(3072 omega^4 \[Pi]^2 zeta^6)-(alpha^2 k2^5 xi^3)/(1152 omega^3 \[Pi]^2 zeta^6)+(alpha^2 k2^5 xi^3)/(3456 omega^2 \[Pi]^2 zeta^6)+(alpha^2 k2^5 xi^3)/(432 omega \[Pi]^2 zeta^6)+(alpha k2^5 xi^4)/(3240 \[Pi]^2 zeta^6)+(alpha k2^5 xi^4)/(10240 omega^4 \[Pi]^2 zeta^6)+(alpha k2^5 xi^4)/(1920 omega^3 \[Pi]^2 zeta^6)+(alpha k2^5 xi^4)/(960 omega^2 \[Pi]^2 zeta^6)+(alpha k2^5 xi^4)/(1080 omega \[Pi]^2 zeta^6)+(k2^5 xi^5)/(648 \[Pi]^2 zeta^6)+(k2^5 xi^5)/(2048 omega^4 \[Pi]^2 zeta^6)+(k2^5 xi^5)/(384 omega^3 \[Pi]^2 zeta^6)+(k2^5 xi^5)/(192 omega^2 \[Pi]^2 zeta^6)+(k2^5 xi^5)/(216 omega \[Pi]^2 zeta^6)-(alpha^4 k2^4)/(810 \[Pi]^2 zeta^5)-(alpha^4 k2^4)/(4608 omega^4 \[Pi]^2 zeta^5)+(alpha^4 k2^4)/(960 omega^2 \[Pi]^2 zeta^5)-(13 alpha^3 k2^4 xi)/(1296 \[Pi]^2 zeta^5)-(7 alpha^3 k2^4 xi)/(23040 omega^4 \[Pi]^2 zeta^5)+(alpha^3 k2^4 xi)/(960 omega^3 \[Pi]^2 zeta^5)+(79 alpha^3 k2^4 xi)/(17280 omega^2 \[Pi]^2 zeta^5)-(alpha^3 k2^4 xi)/(360 omega \[Pi]^2 zeta^5)-(11 alpha^2 k2^4 xi^2)/(540 \[Pi]^2 zeta^5)+(alpha^2 k2^4 xi^2)/(320 omega^4 \[Pi]^2 zeta^5)+(29 alpha^2 k2^4 xi^2)/(2880 omega^3 \[Pi]^2 zeta^5)-(alpha^2 k2^4 xi^2)/(8640 omega^2 \[Pi]^2 zeta^5)-(7 alpha^2 k2^4 xi^2)/(270 omega \[Pi]^2 zeta^5)-(13 alpha k2^4 xi^3)/(648 \[Pi]^2 zeta^5)+(7 alpha k2^4 xi^3)/(7680 omega^4 \[Pi]^2 zeta^5)-(alpha k2^4 xi^3)/(1440 omega^3 \[Pi]^2 zeta^5)-(311 alpha k2^4 xi^3)/(17280 omega^2 \[Pi]^2 zeta^5)-(77 alpha k2^4 xi^3)/(2160 omega \[Pi]^2 zeta^5)-(29 k2^4 xi^4)/(810 \[Pi]^2 zeta^5)-(19 k2^4 xi^4)/(2560 omega^4 \[Pi]^2 zeta^5)-(43 k2^4 xi^4)/(960 omega^3 \[Pi]^2 zeta^5)-(k2^4 xi^4)/(10 omega^2 \[Pi]^2 zeta^5)-(53 k2^4 xi^4)/(540 omega \[Pi]^2 zeta^5)+(31 alpha^3 k2^3)/(3240 \[Pi]^2 zeta^4)+(alpha^3 k2^3)/(2880 omega^4 \[Pi]^2 zeta^4)-(alpha^3 k2^3)/(384 omega^3 \[Pi]^2 zeta^4)-(77 alpha^3 k2^3)/(17280 omega^2 \[Pi]^2 zeta^4)+(alpha^3 k2^3)/(144 omega \[Pi]^2 zeta^4)+(127 alpha^2 k2^3 xi)/(864 \[Pi]^2 zeta^4)-(11 alpha^2 k2^3 xi)/(1440 omega^4 \[Pi]^2 zeta^4)-(227 alpha^2 k2^3 xi)/(5760 omega^3 \[Pi]^2 zeta^4)-(629 alpha^2 k2^3 xi)/(17280 omega^2 \[Pi]^2 zeta^4)+(alpha^2 k2^3 xi)/(10 omega \[Pi]^2 zeta^4)+(77 alpha k2^3 xi^2)/(540 \[Pi]^2 zeta^4)-(7 alpha k2^3 xi^2)/(960 omega^4 \[Pi]^2 zeta^4)-(41 alpha k2^3 xi^2)/(2880 omega^3 \[Pi]^2 zeta^4)+(1147 alpha k2^3 xi^2)/(17280 omega^2 \[Pi]^2 zeta^4)+(293 alpha k2^3 xi^2)/(1440 omega \[Pi]^2 zeta^4)+(113 k2^3 xi^3)/(324 \[Pi]^2 zeta^4)+(3 k2^3 xi^3)/(80 omega^4 \[Pi]^2 zeta^4)+(259 k2^3 xi^3)/(960 omega^3 \[Pi]^2 zeta^4)+(229 k2^3 xi^3)/(320 omega^2 \[Pi]^2 zeta^4)+(33 k2^3 xi^3)/(40 omega \[Pi]^2 zeta^4)-(121 alpha^2 k2^2)/(1080 \[Pi]^2 zeta^3)+(133 alpha^2 k2^2)/(23040 omega^4 \[Pi]^2 zeta^3)+(457 alpha^2 k2^2)/(11520 omega^3 \[Pi]^2 zeta^3)+(67 alpha^2 k2^2)/(1728 omega^2 \[Pi]^2 zeta^3)-(407 alpha^2 k2^2)/(4320 omega \[Pi]^2 zeta^3)-(23 alpha k2^2 xi)/(54 \[Pi]^2 zeta^3)+(199 alpha k2^2 xi)/(11520 omega^4 \[Pi]^2 zeta^3)+(431 alpha k2^2 xi)/(5760 omega^3 \[Pi]^2 zeta^3)-(23 alpha k2^2 xi)/(1728 omega^2 \[Pi]^2 zeta^3)-(325 alpha k2^2 xi)/(864 omega \[Pi]^2 zeta^3)-(1183 k2^2 xi^2)/(1080 \[Pi]^2 zeta^3)-(109 k2^2 xi^2)/(1536 omega^4 \[Pi]^2 zeta^3)-(6761 k2^2 xi^2)/(11520 omega^3 \[Pi]^2 zeta^3)-(7499 k2^2 xi^2)/(4320 omega^2 \[Pi]^2 zeta^3)-(9767 k2^2 xi^2)/(4320 omega \[Pi]^2 zeta^3)+(109 alpha k2)/(360 \[Pi]^2 zeta^2)-(29 alpha k2)/(2304 omega^4 \[Pi]^2 zeta^2)-(91 alpha k2)/(1152 omega^3 \[Pi]^2 zeta^2)-(149 alpha k2)/(2880 omega^2 \[Pi]^2 zeta^2)+(39 alpha k2)/(160 omega \[Pi]^2 zeta^2)+(91 k2 xi)/(72 \[Pi]^2 zeta^2)+(119 k2 xi)/(2304 omega^4 \[Pi]^2 zeta^2)+(565 k2 xi)/(1152 omega^3 \[Pi]^2 zeta^2)+(2251 k2 xi)/(1440 omega^2 \[Pi]^2 zeta^2)+(503 k2 xi)/(240 omega \[Pi]^2 zeta^2)-91/(120 \[Pi]^2 zeta)-1/(96 omega^4 \[Pi]^2 zeta)-15/(128 omega^3 \[Pi]^2 zeta)-7/(16 omega^2 \[Pi]^2 zeta)-25/(32 omega \[Pi]^2 zeta);*)


(* ::Input:: *)
(*(** D - Ghost sector **)*)


(* ::Input:: *)
(*(*** D.1 - Ghost loop contribution to the graviton self energy ***)*)


(* ::Input:: *)
(*selfgh=Expand[-V3gh[a,m,n,e,-k,p,k2,p2,-pk]pgh[e,f,p,p2]V3gh[f,r,s,c,k,p-k,k2,p2+k2-2 pk,pk-k2]pgh[a,c,p-k,p2+k2-2 pk]];*)


(* ::Input:: *)
(*selfgh=Expand[selfgh/.{alpha->alpha/lam^2,xi->xi/lam^2,k[m_]:>lam k[m],pk->lam pk,k2->lam^2 k2}];*)
(*selfgh=Expand[Normal[Series[selfgh,{lam,0,4}]]/.{lam->1}];*)


(* ::Input:: *)
(*selfgh=Expand[selfgh/.rm4];*)
(*selfgh=Expand[selfgh/.r14];*)
(*selfgh=Expand[selfgh/.r04];*)
(*selfgh=Expand[selfgh/.rm3];*)
(*selfgh=Expand[selfgh/.r13];*)
(*selfgh=Expand[selfgh/.r03];*)
(*selfgh=Expand[selfgh/.rm2];*)
(*selfgh=Expand[selfgh/.r12];*)
(*selfgh=Expand[selfgh/.r02];*)
(*selfgh=Expand[selfgh/.rm1];*)
(*selfgh=Expand[selfgh/.r11];*)
(*selfgh=Expand[selfgh/.r01];*)
(*selfgh=Expand[selfgh/.rm0];*)
(*selfgh=Expand[selfgh/.r10];*)
(*selfgh=Expand[I/(8 Pi^2)Coefficient[selfgh,p2,-2]];*)


(* ::Input:: *)
(*(** E - Graviton sector **)*)


(* ::Input:: *)
(*(*** E.1 - Bubble diagram ***)*)


(* ::Input:: *)
(*ris1=Expand[V[c,d,m,n,a,b,k,-p,k2,p2,-pk]P[a,b,ap,bp,p,p2]];*)
(*ris1=Expand[ris1/.{p2-> u p2}];*)
(*ris1=Expand[Normal[Series[ris1,{u,0,-1}]]/.{u->1}];*)
(*ris1=Expand[ris1/.{alpha->alpha/lam^2,xi->xi/lam^2,k[m_]:>lam k[m],pk->lam pk,k2->lam^2 k2}];*)
(*ris1=Expand[Normal[Series[ris1,{lam,0,2}]]];*)


(* ::Input:: *)
(*Coefficient[ris1,lam,-6]*)


(* ::Input:: *)
(*ris2trasla=Expand[1/2 P[c,d,cp,dp,-p,p2]  V[cp,dp,ap,bp,r,s,p+k,-k,p2+k2+2 pk,k2,-pk-k2]];*)
(*ris2trasla=Expand[ris2trasla/.{p2-> u p2}];*)
(*ris2trasla=Expand[Normal[Series[ris2trasla,{u,0,-1}]]/.{u->1}];*)
(*ris2t[c,d,ap,bp,p_,k_,p2_,k2_,pk_]=ris2trasla;*)
(*ris2=ris2t[c,d,ap,bp,p-k,k,p2+k2-2pk,k2,pk-k2];*)
(*ris2=Expand[ris2/.{alpha->alpha/lam^2,xi->xi/lam^2,k[m_]:>lam k[m],pk->lam pk,k2->lam^2 k2}];*)
(*ris2=Expand[Normal[Series[ris2,{lam,0,9}]]];*)


(* ::Input:: *)
(*co[-5]=Coefficient[ris1,lam,-5];*)
(*co[-4]=Coefficient[ris1,lam,-4];*)
(*co[-3]=Coefficient[ris1,lam,-3];*)
(*co[-2]=Coefficient[ris1,lam,-2];*)
(*co[-1]=Coefficient[ris1,lam,-1];*)
(*co[0]=Coefficient[ris1,lam,0];*)
(*co[1]=Coefficient[ris1,lam,1];*)
(*co[2]=Coefficient[ris1,lam,2];*)
(*do[2]=Coefficient[ris2,lam,2];*)
(*do[3]=Coefficient[ris2,lam,3];*)
(*do[4]=Coefficient[ris2,lam,4];*)
(*do[5]=Coefficient[ris2,lam,5];*)
(*do[6]=Coefficient[ris2,lam,6];*)
(*do[7]=Coefficient[ris2,lam,7];*)
(*do[8]=Coefficient[ris2,lam,8];*)
(*do[9]=Coefficient[ris2,lam,9];*)


(* ::Input:: *)
(*DateList[]*)
(*w1=Expand[co[2]do[2]];*)
(*DateList[]*)
(*w2=Expand[co[1]do[3]];*)
(*DateList[]*)
(*w3=Expand[co[0]do[4]];*)
(*DateList[]*)
(*w4=Expand[co[-1]do[5]];*)
(*DateList[]*)
(*w5=Expand[co[-2]do[6]];*)
(*DateList[]*)
(*w6=Expand[co[-3]do[7]];*)
(*DateList[]*)
(*w7=Expand[co[-4]do[8]];*)
(*DateList[]*)
(*w8=Expand[co[-5] do[9]];*)
(*DateList[]*)
(*tot=Expand[w1+w2+w3+w4+w5+w6+w7+w8];*)


(* ::Input:: *)
(*ris=Expand[tot/.rm4];*)
(*ris=Expand[ris/.r14];*)
(*ris=Expand[ris/.r04];*)
(*ris=Expand[ris/.rm3];*)
(*ris=Expand[ris/.r13];*)
(*ris=Expand[ris/.r03];*)
(*ris=Expand[ris/.rm2];*)
(*ris=Expand[ris/.r12];*)
(*ris=Expand[ris/.r02];*)
(*ris=Expand[ris/.rm1];*)
(*ris=Expand[ris/.r11];*)
(*ris=Expand[ris/.r01];*)
(*ris=Expand[ris/.rm0];*)
(*ris=Expand[ris/.r10];*)
(*bolla=Expand[I/(8 Pi^2)Coefficient[ris,p2,-2]];*)


(* ::Input:: *)
(*(** F - Scalar fields **)*)


(* ::Input:: *)
(*(*** F.1 - Scalar vertices ***)*)


(* ::Input:: *)
(*LL=Expand[-(p[m]q[n]+p[n]q[m])/2 sqrtg[a1,a2,p3] ginv[m,n,a4,a5]];*)


(* ::Input:: *)
(*Expand[kappa Coefficient[LL,kappa,1]];*)
(*Expand[%/.{h[a_,b_][]:>delta[a,z]delta[b,w]}];*)
(*Vs31[z_,w_,p_,q_,pq_]=ExpandAll[%];*)
(*Vs31a[z_,w_,p_,q_,pq_]=ExpandAll[I Vs31[z,w,p,q,pq]];*)
(*Vs3[z_,w_,p_,q_,pq_]=ExpandAll[1/2(Vs31a[z,w,p,q,pq]+Vs31a[w,z,p,q,pq])];*)


(* ::Input:: *)
(*Expand[kappa^2 Coefficient[LL,kappa,2]];*)
(*Expand[%/.{A___ h[a_,b_][]:>A delta[a,zp]delta[b,wp],A___ h[a_,b_][]^2:>A h[a,b][] delta[a,zp]delta[b,wp]}];*)
(*Expand[%/.{h[a_,b_][]:>delta[a,z]delta[b,w]}];*)
(*Vs41[z_,w_,zp_,wp_,p_,q_,pq_]=ExpandAll[%];*)
(*Vs41a[z_,w_,zp_,wp_,p_,q_,pq_]=ExpandAll[I Vs41[z,w,zp,wp,p,q,pq]];*)
(*Vs42[z_,w_,m_,n_,p_,q_,pq_]=ExpandAll[1/2(Vs41a[z,w,m,n,p,q,pq]+Vs41a[w,z,m,n,p,q,pq])];*)
(*Vs43[z_,w_,m_,n_,p_,q_,pq_]=ExpandAll[1/2(Vs42[z,w,m,n,p,q,pq]+Vs42[z,w,n,m,p,q,pq])];*)
(*Vs4[z_,w_,m_,n_,p_,q_,pq_]=Expand[Vs43[z,w,m,n,p,q,pq]+Vs43[m,n,z,w,p,q,pq]];*)


(* ::Input:: *)
(*Expand[kappa^3 Coefficient[LL,kappa,3]];*)
(*Expand[%/.{A___ h[a_,b_][]:>A delta[a,zp]delta[b,wp],A___ h[a_,b_][]^2:>A h[a,b][] delta[a,zp]delta[b,wp]}];*)
(*Expand[%/.{A___ h[a_,b_][]:>A delta[a,zq]delta[b,wq],A___ h[a_,b_][]^2:>A h[a,b][] delta[a,zq]delta[b,wq]}];*)
(*Expand[%/.{h[a_,b_][]:>delta[a,z]delta[b,w]}];*)
(*Vs51[z_,w_,zp_,wp_,zq_,wq_,p_,q_,pq_]=ExpandAll[%];*)
(*Vs51a[z_,w_,zp_,wp_,zq_,wq_,p_,q_,pq_]=ExpandAll[I Vs51[z,w,zp,wp,zq,wq,p,q,pq]];*)
(*Vs52[z_,w_,m_,n_,r_,s_,p_,q_,pq_]=ExpandAll[1/2(Vs51a[z,w,m,n,r,s,p,q,pq]+Vs51a[w,z,m,n,r,s,p,q,pq])];*)
(*Vs53[z_,w_,m_,n_,r_,s_,p_,q_,pq_]=ExpandAll[1/2(Vs52[z,w,m,n,r,s,p,q,pq]+Vs52[z,w,n,m,r,s,p,q,pq])];*)
(*Vs54[z_,w_,m_,n_,r_,s_,p_,q_,pq_]=Expand[1/2(Vs53[z,w,m,n,r,s,p,q,pq]+Vs53[z,w,m,n,s,r,p,q,pq])];*)
(*Vs5[z_,w_,m_,n_,r_,s_,p_,q_,pq_]=ExpandAll[Vs54[z,w,m,n,r,s,p,q,pq]+Vs54[m,n,z,w,r,s,p,q,pq]+Vs54[r,s,m,n,z,w,p,q,pq]+Vs54[z,w,r,s,m,n,p,q,pq]+Vs54[r,s,z,w,m,n,p,q,pq]+Vs54[m,n,r,s,z,w,p,q,pq]];*)


(* ::Input:: *)
(*(*** F.2 - Scalar bubble ***)*)


(* ::Input:: *)
(*scal=Expand[1/2 I/p2 I/(p2+k2+2pk)Vs3[m,n,p,-p-k,-p2-pk]Vs3[r,s,p+k,-p,-p2-pk]];*)
(*scal=Expand[scal/.{k[m_]:>lam k[m],k2->lam^2 k2,pk->lam pk}];*)
(*ris=Expand[1/4! D[scal,{lam,4}]];*)
(*ris=Expand[ris/.{lam->0}];*)
(*ris=Expand[ris/.rm4];*)
(*ris=Expand[ris/.r14];*)
(*ris=Expand[ris/.r04];*)
(*ris=Expand[ris/.rm3];*)
(*ris=Expand[ris/.r13];*)
(*ris=Expand[ris/.r03];*)
(*ris=Expand[ris/.rm2];*)
(*ris=Expand[ris/.r12];*)
(*ris=Expand[ris/.r02];*)
(*ris=Expand[ris/.rm1];*)
(*ris=Expand[ris/.r11];*)
(*ris=Expand[ris/.r01];*)
(*ris=Expand[ris/.rm0];*)
(*ris=Expand[ris/.r10];*)
(*scal=Expand[I/(8 Pi^2)Coefficient[ris,p2,-2]];*)
(*Expand[scal-1/(960 \[Pi]^2) InvRic2[m,n,r,s,k,k2]-1/(1920 \[Pi]^2) InvR2[m,n,r,s,k,k2]]*)


(* ::Input:: *)
(*(** G - Analysis of the result **)*)


(* ::Input:: *)
(*(*** G.1 - Two-point function ***)*)


(* ::Input:: *)
(*Lagra=Expand[Lagra1+Lagra2g];*)
(*Vert1=1/kappa Coefficient[Lagra,kappa,-1];*)
(*Vert2=Coefficient[Lagra,kappa,0];Expand[Vert2/.{A___ h[a_,b_][]:>A delta[a,zp]delta[b,wp],A___ h[a_,b_][m_]:>-I A p[m]delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_]:>- A p[m]p[n] delta[a,zp]delta[b,wp],A___ h[a_,b_][]^2:>A h[a,b][] delta[a,zp]delta[b,wp],A___ h[a_,b_][m_]^2:>-I A h[a,b][m] p[m]delta[a,zp]delta[b,wp],A___ h[a_,b_][m_,n_]^2:>- A h[a,b][m,n] p[m]p[n] delta[a,zp]delta[b,wp]}];*)
(*Expand[%/.{h[a_,b_][]:>delta[a,z]delta[b,w],h[a_,b_][m_]:>I p[m]delta[a,z]delta[b,w],h[a_,b_][m_,n_]:>- p[m]p[n] delta[a,z]delta[b,w]}];*)
(*V2a[z_,w_,zp_,wp_,p_,p2_]=ExpandAll[I %];*)
(*V2b[m_,n_,r_,s_,p_,p2_]=ExpandAll[1/2(V2a[m,n,r,s,p,p2]+V2a[n,m,r,s,p,p2])];*)
(*V2c[m_,n_,r_,s_,p_,p2_]=ExpandAll[1/2(V2b[m,n,r,s,p,p2]+V2b[m,n,s,r,p,p2])];*)
(*V2[m_,n_,r_,s_,p_,p2_]=ExpandAll[V2c[m,n,r,s,p,p2]+V2c[r,s,m,n,p,p2]];*)
(*T[a_,b_,m_,n_]:=kappa^3(a1 k2 (delta[a,m]delta[b,n]+delta[a,n]delta[b,m])+a2 k2 delta[m,n]delta[a,b]+a3 delta[a,b]k[m]k[n]+a4 delta[m,n]k[a]k[b]+a5 (delta[n,a]k[b]k[m]+delta[m,a]k[b]k[n]+delta[m,b]k[a]k[n]+delta[n,b]k[a]k[m])+a6 k[a]k[b]k[m]k[n])*)


(* ::Input:: *)
(*ris=Expand[bolla+selfgh+Ns scal+Deltaalpha/(16 Pi^2) (InvRic2[m,n,r,s,k,k2]-1/3 InvR2[m,n,r,s,k,k2]) -(Deltaxi/6)/(16 Pi^2) InvR2[m,n,r,s,k,k2]+ 1/(2 kappa)V2[r,s,mm,nn,k,k2]T[mm,nn,m,n]+1/(2 kappa)V2[m,n,mm,nn,k,k2]T[mm,nn,r,s]]*)