PhyAmateur
- 103
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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.
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.