1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Maggiore p.52

  1. Jan 31, 2009 #1


    User Avatar

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Maggiore p.52
  1. Is <p>_c = -<p>? (Replies: 10)

  2. Calculating d<p>/dt (Replies: 3)