(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. 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currentKernel; ] :[font = input; noPageBreak; preserveAspect] Off[General::spell]; Off[General::spell1]; :[font = section; inactive; Cclosed; preserveAspect; startGroup] ================================ Load FeynCalc: :[font = input; inactive; preserveAspect] Get["/users/smuphy/olness/mathload/FeynCalc2/FeynCalc.m"] :[font = input; inactive; preserveAspect; endGroup] Get["/users/smuphy/olness/mathload/FeynCalc2/FeynCalc2.0b07.m"] :[font = input; preserveAspect; startGroup] Get["/users/smuphy/olness/mathload/FeynCalc2/FeynCalc2.0b13.m"] :[font = print; inactive; preserveAspect] :[font = print; inactive; preserveAspect; endGroup] FeynCalc 2.0beta13 (November 1993) | :[font = section; inactive; preserveAspect; startGroup] ================================ Check with Halzen :[font = input; preserveAspect; startGroup] {p1s,p2s,p3s,p4s}=Map[DiracSlash,{p1,p2,p3,p4}] :[font = output; output; inactive; preserveAspect; endGroup] {"gs[p1]", "gs[p2]", "gs[p3]", "gs[p4]"} ;[o] {gs[p1], gs[p2], gs[p3], gs[p4]} :[font = input; preserveAspect; startGroup] {gm,gn,gm1,gm2}=Map[DiracMatrix,{mu,nu,mu1,mu2}] :[font = output; output; inactive; preserveAspect; endGroup] {"ga[mu]", "ga[nu]", "ga[mu1]", "ga[mu2]"} ;[o] {ga[mu], ga[nu], ga[mu1], ga[mu2]} :[font = input; preserveAspect; startGroup] Tr[ gm.p1s.gn.p2s ] :[font = output; output; inactive; preserveAspect; endGroup] 4*(-("g"[mu, nu]*p1"."p2) + p1"["nu"]"*p2"["mu"]" + p1"["mu"]"*p2"["nu"]") ;[o] 4 (-(g[mu, nu] p1.p2) + p1[nu] p2[mu] + p1[mu] p2[nu]) :[font = input; preserveAspect; startGroup] 4 Tr[ gm.DiracGamma[7].p1s.gn.DiracGamma[7].p2s ] - 2Tr[ gm.p1s.gn.p2s ] //Expand :[font = output; output; inactive; preserveAspect; endGroup] 8*I*"eps"[mu, nu, p1, p2] ;[o] 8 I eps[mu, nu, p1, p2] :[font = input; preserveAspect; startGroup] Contract[ Tr[ gm.p1s.gn.p2s ] Tr[ gm.p3s.gn.p4s ] ] :[font = output; output; inactive; preserveAspect; endGroup] 32*p1"."p4*p2"."p3 + 32*p1"."p3*p2"."p4 ;[o] 32 p1.p4 p2.p3 + 32 p1.p3 p2.p4 :[font = input; preserveAspect; startGroup] Contract[ Tr[ gm.p1s.gn.DiracGamma[5].p2s ] Tr[ gm.p3s.gn.DiracGamma[5].p4s ] , EpsContract->True] //Simplify :[font = output; output; inactive; preserveAspect; endGroup] -32*(p1"."p4*p2"."p3 - p1"."p3*p2"."p4) ;[o] -32 (p1.p4 p2.p3 - p1.p3 p2.p4) :[font = input; preserveAspect; startGroup] Contract[ 4 Tr[ gm.DiracGamma[7].p1s.gn.DiracGamma[7].p2s ] * 4 Tr[ gm.DiracGamma[7].p3s.gn.DiracGamma[7].p4s ] , EpsContract->True] //Simplify :[font = output; output; inactive; preserveAspect; endGroup] 256*p1"."p3*p2"."p4 ;[o] 256 p1.p3 p2.p4 :[font = input; preserveAspect; startGroup] Tr[ Spinor[p,m].Spinor[p,m] ] //DiracSimplify :[font = output; output; inactive; preserveAspect; endGroup] 4*Feyn`Calc`Main`fcdot2["u[p, m]", "u[p, m]"] ;[o] 4 u[p, m] u[p, m] :[font = input; preserveAspect; startGroup] Tr[ DiracGamma[5].gm.gn.gm1.gm2 ] :[font = output; output; inactive; preserveAspect; endGroup; endGroup] -4*I*"eps"[mu, mu1, mu2, nu] ;[o] -4 I eps[mu, mu1, mu2, nu] :[font = input; preserveAspect; startGroup] Tr[DiracMatrix[a1,a2,a3,a4,5]] :[font = output; output; inactive; preserveAspect; endGroup] -4*I*"eps"[a1, a2, a3, a4] ;[o] -4 I eps[a1, a2, a3, a4] :[font = input; preserveAspect; startGroup] Tr[DiracMatrix[a1,a2,a3,a4,a5,a6,5]] :[font = output; output; inactive; preserveAspect; endGroup] 4*(-I*"eps"[a3, a4, a5, a6]*"g"[a1, a2] + I*"eps"[a2, a4, a5, a6]*"g"[a1, a3] - I*"eps"[a1, a4, a5, a6]*"g"[a2, a3] - I*"eps"[a1, a2, a3, a6]*"g"[a4, a5] + I*"eps"[a1, a2, a3, a5]*"g"[a4, a6] - I*"eps"[a1, a2, a3, a4]*"g"[a5, a6]) ;[o] 4 (-I eps[a3, a4, a5, a6] g[a1, a2] + I eps[a2, a4, a5, a6] g[a1, a3] - I eps[a1, a4, a5, a6] g[a2, a3] - I eps[a1, a2, a3, a6] g[a4, a5] + I eps[a1, a2, a3, a5] g[a4, a6] - I eps[a1, a2, a3, a4] g[a5, a6]) :[font = input; preserveAspect; startGroup] (tmp= Tr[DiracMatrix[a1,a2,a3,a4,a5,a6,a7,a8,5]]) //Timing //First :[font = output; output; inactive; preserveAspect; endGroup] 15.96666666666667*"s" ;[o] 16. s :[font = input; preserveAspect; startGroup] tmp //Last //Length :[font = output; output; inactive; preserveAspect; endGroup] 105 ;[o] 105 :[font = section; inactive; preserveAspect] ================================ Do Traces from Ch6 Halzen :[font = input; preserveAspect; startGroup] temp1= Tr[ (DiracSlash[kp]+m) .DiracMatrix[mu] .(DiracSlash[k ]+m) .DiracMatrix[nu] ] :[font = output; output; inactive; preserveAspect; endGroup] 4*(m^2*"g"[mu, nu] - "g"[mu, nu]*k"."kp + k"["nu"]"*kp"["mu"]" + k"["mu"]"*kp"["nu"]") ;[o] 2 4 (m g[mu, nu] - g[mu, nu] k.kp + k[nu] kp[mu] + k[mu] kp[nu]) :[font = input; preserveAspect; startGroup] temp2= Tr[ (DiracSlash[pp]+m) .DiracMatrix[mu] .(DiracSlash[p ]+m) .DiracMatrix[nu] ] :[font = output; output; inactive; preserveAspect; endGroup] 4*(m^2*"g"[mu, nu] - "g"[mu, nu]*p"."pp + p"["nu"]"*pp"["mu"]" + p"["mu"]"*pp"["nu"]") ;[o] 2 4 (m g[mu, nu] - g[mu, nu] p.pp + p[nu] pp[mu] + p[mu] pp[nu]) :[font = input; preserveAspect; startGroup] temp3= temp1 temp2 //Contract :[font = output; output; inactive; preserveAspect; endGroup] 64*m^4 - 32*m^2*k"."kp + 32*k"."pp*kp"."p + 32*k"."p*kp"."pp - 32*m^2*p"."pp ;[o] 4 2 2 64 m - 32 m k.kp + 32 k.pp kp.p + 32 k.p kp.pp - 32 m p.pp :[font = subsection; inactive; preserveAspect; startGroup] ================================ Examine Mandelstam Variables :[font = input; preserveAspect] SetMandelstam[s,t,u,p,k,-pp,-kp,m,m,m,m]; :[font = input; preserveAspect; startGroup] ( {ScalarProduct[p+k,p+k] ,ScalarProduct[p-pp,p-pp] ,ScalarProduct[p-kp,p-kp]} //ExpandScalarProduct //Simplify ) :[font = output; output; inactive; preserveAspect; endGroup; endGroup] {s, t, u} ;[o] {s, t, u} :[font = input; preserveAspect; startGroup] temp3 //Simplify :[font = output; output; inactive; preserveAspect; endGroup] 8*(8*m^4 - 4*m^2*s + s^2 + 4*m^2*t - 4*m^2*u + u^2) ;[o] 4 2 2 2 2 2 8 (8 m - 4 m s + s + 4 m t - 4 m u + u ) :[font = input; preserveAspect; startGroup] temp4= temp3 /.{m->0} //Simplify :[font = output; output; inactive; preserveAspect; endGroup] 8*(s^2 + u^2) ;[o] 2 2 8 (s + u ) :[font = input; preserveAspect; startGroup] denom= (ScalarProduct[k-kp,k-kp])^2 //ExpandScalarProduct :[font = output; output; inactive; preserveAspect; endGroup] t^2 ;[o] 2 t :[font = input; preserveAspect; startGroup] result= temp4/denom e^4/4 :[font = output; output; inactive; preserveAspect; endGroup] (2*e^4*(s^2 + u^2))/t^2 ;[o] 4 2 2 2 e (s + u ) -------------- 2 t ^*)