I'm reading Zee book on quantum field theory.(adsbygoogle = window.adsbygoogle || []).push({});

He wants to explain that pion is the goldstone boson arising from the spontaneous simmetry breaking of the chiral symmetry.

So he

start with the weak decay

[itex]\pi^{-} \rightarrow \bar{\nu} + e^{-} [/itex]

and write this equation

[itex] <0|J^{\mu}_{5}|k>=f k^{\mu}[/itex] (1),

where [itex] k [/itex] is the momentum of the pion.

Then, of course, if you act with [itex] k_{\mu} [/itex] on the left, you get

[itex] k_{\mu }<0|J^{\mu}_{5}|k>=f m _{\pi} [/itex] (2)

and we see that if we consider the pion as a massless spin 0 particle, it is a good candidate for a goldstone boson associated with the spontaneous breaking of the chiral symmetry, because it then follows that

[itex] \partial_{\mu} J_{5}^{\mu} = 0 [/itex]

My questions are:

-why in (1) he wrote only the axial current and he doesn't write something like

[itex] <0|J^{\mu}-J^{\mu}_{5}|k> [/itex]

?

-why the right hand side of (1) is just a vector while the left hand side is a pseudovector?

Thank you!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Pion as a goldstone boson

**Physics Forums | Science Articles, Homework Help, Discussion**