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Global Symmetries

  1. Mar 13, 2013 #1
    1.jpg
    2.jpg

    I don't know how (1.10) pops up and why the ##T^a##s satisfy the Lie algebra.
    Is there any physical intuition?

    Any comment would be very appreciated!
     
  2. jcsd
  3. Mar 14, 2013 #2
    The finite transformation is the exponential
    [tex]
    \exp(-i \theta_a T^a)
    [/tex]
    here [itex]\theta[/itex] is the generator's parameter and [itex]T[/itex] is the generator of the transformation. This is to linear order
    [tex]
    = 1 - i\theta_{a}T^{a}
    [/tex]
    This is like in quantum mechanics where for a finite translation you would write
    [tex]
    \exp(-ia\hat{p}) \rightarrow 1 - i a \hat{p}
    [/tex]
    for an infinitesimal translation. But you need to know the action of the generator on the coordinates, i.e. how does [itex]x[/itex] look after it gets acted on by this transformation.
     
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