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Relative velocity of beams

  1. Oct 26, 2014 #1
    How come relative velocity of the beams can be expressed by
    [itex]v_{12} = \left| \vec{v}_1 - \vec{v}_2 \right| = \left|\frac{\vec{p}_1}{E_1} - \frac{\vec{p}_2}{E_2}\right|[/itex]
    where [itex]\vec{p}_{1,2}[/itex] and [itex]E_{1,2}[/itex] is the momenta and energies of incoming particles, respectively?
    Similar equation is in Peskin & Schroeder, p 105. The dimensions don't add up ...
     
    Last edited: Oct 26, 2014
  2. jcsd
  3. Oct 26, 2014 #2

    WannabeNewton

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    Science Advisor

    Velocity is dimensionless; ##p## and ##E## both have dimension 1. The desired expression follows essentially from the definition of ##p## relative to a Lorentz frame.
     
  4. Oct 26, 2014 #3
    doh... natural units... thx
     
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