M2 - (Pi - Pi)2 - M2 - (Pi -P2)2 - ie Ai2 - (Pi +P2)2 -ie. Finally, the S-matrix is obtained by application of the projection operator Ptotai-First, replace the energy conserving 6 function by its integral representation
<$(pio + P20 - p'10 ~ P20) = lim f dr ¿too+P»o-p'10-pSo) - ,
T—too ¿TT J_rp and, holding T fixed, consider a typical initial time t much earlier than -T, so that -T > t —► -00. The integral over pio (for example) then becomes
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