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Prove Lorentz invariance for momentum 4-vector

  1. May 5, 2016 #1
    1. The problem statement, all variables and given/known data
    I am meant to show that the following equation is manifestly Lorentz invariant:
    $$\frac{dp^{\mu}}{d\tau}=\frac{q}{mc}F^{\mu\nu}p_{\nu}$$

    2. Relevant equations
    I am given that ##F^{\mu\nu}## is a tensor of rank two.

    3. The attempt at a solution
    I was thinking about doing a Lorents transformation to this four vector, but I don't know what this would yield.
     
  2. jcsd
  3. May 5, 2016 #2
    Well then why not try it? When we say that an equation is Lorentz invariant, what we mean is that it holds true in all (inertial) reference frames accessible via a Lorentz transformation. So, that means that you have to show that if
    [tex]\frac{dp^{\mu}}{d\tau}=\frac{q}{mc}F^{\mu\nu}p_{\nu}[/tex]
    then
    [tex]\frac{dp^{\mu'}}{d\tau}=\frac{q}{mc}F^{\mu'\nu'}p_{\nu'}[/tex]
    is also true.
     
  4. May 11, 2016 #3
    You're right! Thank you so much.
     
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