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Maggiore p.52

  1. Jan 31, 2009 #1

    PJK

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    I have a question about an equation in Maggiore's Modern Introd. to Quantum Field Theory p.52:
    [tex]\delta x^\mu = w^\mu_\nu x^\mu = \sum_{\rho < \sigma} A^\mu_{(\rho \sigma)} w^{\rho \sigma}[/tex]
    where the A is defined as
    [tex]A^\mu_{(\rho \sigma)}=\delta^{\mu}_{\rho}x_\sigma - \delta^\mu_\sigma x_\rho[/tex]

    If I do this calculation I always end up with a factor 3 on the right hand side times the desired result. Is this an error in the book? Or am I doing something wrong?
     
  2. jcsd
  3. Jan 31, 2009 #2
    The author is correct. Usually 'Aw' is written as '1/2 Aw' without specification that one indice is smaller than the other (A and w are antisymmetric so this is possible).

    It's a bit baffling that the author defines the rotations like that though. I think the x's in the definition of A should be replaced by the metric 'g' that contracts with 'x' to get those expressions. That way iA would be a generator for the SO(4) vectorial representation.
     
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