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Σ Model, from not obvious to obvious?

  1. Feb 6, 2015 #1
    Georgi in his book, for reference: http://www.people.fas.harvard.edu/~hgeorgi/weak.pdf he says that it is not obvious that the form of $$\Sigma = \sigma + i\tau_a\pi_a$$ is preserved under (2.6.6) $$ \delta \Sigma = i \epsilon_L^aT_a \Sigma - i \Sigma \epsilon_R^aT_a$$

    But then he said, "But it is true, and you can work out by explicit calculation the transformations of the $\sigma$ and $\pi _a$ fields":

    $$\delta \sigma = \epsilon_5^a \pi_a$$
    $$\delta \pi_a = - \epsilon_{abc}\epsilon^b\pi_c - \epsilon_5^a \sigma$$

    But I have no idea how after what he wrote it became obvious? It is still not obvious to me how it is preserved though he saying it must be.
  2. jcsd
  3. Feb 8, 2015 #2
    I don't think he wants to say that it becomes obvious but simply that if you actually do the calculation with the change of the ##\sigma## and ##\pi_a## fields that you listed before you'll find that it is actually invariant. By ''obvious'' he probably means that can be seen by eye, without doing the explicit calculation.
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