Name: Abhijit Date: 11/06/18-08:43:46 AM Z

I used Dopolariation twice while doing compton scattering.
A = DoPolarizationSums[Ma2, k, 0]
B=DoPolarizationSums[A, k’, 0]

Ma2 is compton aplitude square which was obtianed successfully.
A seems to give good result

-((e^4 tr((Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\CenterDot+m).(Overscript[\[Gamma], _]\[CenterDot]Overscript\[CurlyEpsilon], _).(Overscript[\[Gamma], _]\[CenterDot]Overscript[p^\[Prime], _]+m).(Overscript[\[Gamma], _]\[CenterDot]Overscript[\[CurlyEpsilon], _]^*(k^\[Prime])).(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^\[Sigma]))/(16 ((Overscript[k, _]\[CenterDot]Overscript[p, _]))^2))-(e^4 tr((Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]+m).(Overscript[\[Gamma], _]\[CenterDot]Overscript\[CurlyEpsilon], _).(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\[CenterDot]Overscript[p^\[Prime], _]+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\CenterDot+m).(Overscript[\[Gamma], _]\[CenterDot]Overscript[\[CurlyEpsilon], _]^*(k^\[Prime]))))/(16 ((Overscript[p, _]\[CenterDot]Overscript[k^\[Prime], _]))^2)+(e^4 tr((Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\CenterDot+m).(Overscript[\[Gamma], _]\[CenterDot]Overscript\[CurlyEpsilon], _).(Overscript[\[Gamma], _]\[CenterDot]Overscript[p^\[Prime], _]+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\CenterDot+m).(Overscript[\[Gamma], _]\[CenterDot]Overscript[\[CurlyEpsilon], _]^*(k^\[Prime]))))/(16 (Overscript[k, _]\[CenterDot]Overscript[p, _]) (Overscript[p, _]\[CenterDot]Overscript[k^\[Prime], _]))+(e^4 tr((Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]+m).(Overscript[\[Gamma], _]\[CenterDot]Overscript\[CurlyEpsilon], _).(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\[CenterDot]Overscript[p^\[Prime], _]+m).(Overscript[\[Gamma], _]\[CenterDot]Overscript[\[CurlyEpsilon], _]^*(k^\[Prime])).(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^\[Sigma]))/(16 (Overscript[k, _]\[CenterDot]Overscript[p, _]) (Overscript[p, _]\[CenterDot]Overscript[k^\[Prime], _]))
B GIVES WIERD RESULT

-((e^4 tr(-(Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]+m).Overscript[\[Gamma], _]^$AL$13451\InvisibleApplication.(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\[CenterDot]Overscript[p^\[Prime], _]+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^$AL$13451\InvisibleApplication))/(16 ((Overscript[p, _]\[CenterDot]Overscript[k^\[Prime], _]))^2))-(e^4 tr(-(Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^$AL$13449\InvisibleApplication.(Overscript[\[Gamma], _]\[CenterDot]Overscript[p^\[Prime], _]+m).Overscript[\[Gamma], _]^$AL$13449\InvisibleApplication.(Overscript[\[Gamma], _]\CenterDot+m).Ove
 rscript[\[Gamma], _]^\[Sigma]))/(16 ((Overscript[k, _]\[CenterDot]Overscript[p, _]))^2)+(e^4 tr(-(Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^$AL$13453\InvisibleApplication.(Overscript[\[Gamma], _]\[CenterDot]Overscript[p^\[Prime], _]+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^$AL$13453\InvisibleApplication))/(16 (Overscript[k, _]\[CenterDot]Overscript[p, _]) (Overscript[p, _]\[CenterDot]Overscript[k^\[Prime], _]))+(e^4 tr(-(Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]+m).Overscript[\[Gamma], _]^$AL$13455\InvisibleApplication.(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^\[Sigma].(Overscript[\[Gamma], _]\[CenterDot]Overscript[p^\[Prime], _]+m).Overscrip
 t[\[Gamma], _]^$AL$13455\InvisibleApplication.(Overscript[\[Gamma], _]\CenterDot+m).Overscript[\[Gamma], _]^\[Sigma]))/(16 (Overscript[k, _]\[CenterDot]Overscript[p, _]) (Overscript[p, _]\[CenterDot]Overscript[k^\[Prime], _]))