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Homework Help: Relativistic Invariance

  1. Oct 10, 2007 #1
    1. The problem statement, all variables and given/known data
    Prove that the quantity [itex]2EN^2 dx^3[/itex] is a relativistic invariant.


    2. Relevant equations

    Well we want to prove that this quantity is the same in all inercial frames.
    My doubt is with the energy transformation,

    [tex]E=\gamma E_0[/tex]

    does it transforms like that? If yes,


    [tex]dx^3=\frac{dx_0^3}{\gamma}[/tex]

    [tex]2EN^2 dx^3=2 \gamma E_0 N^2 \frac{dx^3}{\gamma}=2E_0 N^2 dx_0^3[/tex]

    and its done...?

    Thanks
     
    Last edited: Oct 10, 2007
  2. jcsd
  3. Oct 11, 2007 #2

    dextercioby

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    Science Advisor
    Homework Helper

    Do you know the covariant formalism ? If you do, you might know that [tex]p_{\mu}x^{\mu} [/tex] is a Lorentz scalar. Assume a Lorentz boost in the positive Ox direction...Can you continue from here ?

    P.S. What does N stand for ?
     
  4. Oct 12, 2007 #3
    I have done it. That result is correct. Thanks a lot.
    By the way N stands for a normalization factor that cames, I guess, from the wave function.
     
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