I don't understand these sentences from Peskin:(adsbygoogle = window.adsbygoogle || []).push({});

"At long wavelength (*why long wavelength?*), the Goldstone bosons become infinitesimal symmetry rotations of the vacuum, ##Q^a|0 \rangle##, where ##Q^a## is the global charge associated with ##J^{\mu a}##. Thus, the operators ##J^{\mu a}## have the correct quantum numbers to create Goldstone boson state. In general, there will be a current ##J^{\mu a}## that can create or destroy this boson; we can parametrize the corresponding matrix element as $$\langle 0| J^{\mu a} | \pi_k(p) \rangle = -i p^\mu F^a{}_k e^{-ip \cdot x}$$, where ##p^{\mu}## is the on-shell momentum of the boson and ##F^a{}_k## is a matrix of constants. The elements ##F^a{}_k## vanish when ##a## deontes a generator of an unbroken symmetry.""

I don't understand every single sentence here. Can anybody explain. It is from Peskin&Schroeder 20.1 formula 20.46. Thanks.

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# Goldstone boson state, conserved current

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