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Feynmann diagram

  1. Jun 9, 2007 #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations
    Hi, I'm studying Feynmann diagrams; electron-positron scattering.
    If the 4-momentum of the incoming electron (positron) is p1 (p2) and of the outgoing electron (positron) is p3 (p4), momentum conservation gives
    p1 + p2 = p3 + p4

    If you now consider the scattering in the frame where the threemomentum of the incoming positron = 0. Why does then defining threemomentum p4=p3 imply that they equal 0?
    And why does defining p3*p4=0 (three vectors) imply that p3(threevector)=0 or p4=0?

    3. The attempt at a solution

    I tried: 4-vectors: p1+p2=p3+p4
    square this: (p1)^2 + (p2)^2 + 2*p1*p2= (p3)^2 + (p4)^2 + 2*p3*p4

    (p1)^2=(p3)^2=m (electron mass)
    (p2)^2=(p4)^2=M (positron mass)

    So: p1*p2=p3*p4
    The lab frame condition gives:
    p1(0)*p2(0)=p3(0)*p4(0)-p3*p4(three-vectors)

    But what are the next steps????
    (I hope I made clear the problem, it isn't very readable I'm afraid....)
     
  2. jcsd
  3. Jun 10, 2007 #2
    I'll try a little LATEX to make the problem more clear:

    [tex]
    p_{1} + p_{2} = p_{3} + p_{4}
    [/tex]
    These are four vectors of the in- and going momenta

    You take the frame where the threemomentum [tex]p_{2}=0[/tex]

    Questions:
    1) Why does then defining threemomentum [tex]p_{4}=p_{3}[/tex] imply that [tex]p_{4}=p_{3}=0[/tex]? (threemomenta!)
    And why does defining [tex]p_{3}*p_{4}=0[/tex] (three vectors) imply that [tex]p_{3}=0 or p_{4}=0[/tex]?

    3. The attempt at a solution

    I tried: 4-vectors: [tex]
    p_{1} + p_{2} = p_{3} + p_{4}
    [/tex]
    square this: [tex](p_{1})^(2) + (p_{2})^(2) + 2p_{1}p_{2}= (p_{3})^(2) + (p_{4})^(2) + 2p_{3}p_{4}
    //
    (p_{1})^(2)=(p_{3})^(2)=m (electron mass)
    (p_{2})^(2)=(p_{4})^(2)=M (positron mass)
    [/tex]
    So: [tex]p_{1}p_{2}=p_{3}*p_{4}[/tex]
    The lab frame condition gives:
    [tex]p_{1}^{0}p_{2}^{0}=p_{3}^{0}p_{4}^{0}-p_{3}*p_{4}(three-vectors)[/tex]

    But what are the next steps????
    (I hope I made clear the problem, it isn't very readable I'm afraid....)
     
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