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Lorentz invariant measure

  1. Nov 11, 2009 #1

    I have a question about Lorentz invariant measures,
    consider an integral of the form:
    [tex]\int d\mu(p) f(\Lambda^{-1}p)[/tex]

    where [tex]d\mu(p) = d^3{\bf p}/(2\pi)^3(2p_0)^3[/tex] is the Lorentz invariant measure.

    Now to simplify this I can make a change of coordinates

    [tex]\int d\mu(\Lambda q) f(q)[/tex]

    can I then simplify this such that:

    [tex]\int d\mu(q) f(q)[/tex]

    because this is Lorentz invariant or am I cheating?


  2. jcsd
  3. Nov 12, 2009 #2
    Yes, you can. Compare with Euclidean 2D case where [tex]d\mu = r dr d\phi[/tex] and [tex]\Lambda[/tex] is a rotation about the center.
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