Re: Weinberg on the anomaly
- From: Al.Rivero@xxxxxxxxx
- Date: Thu, 30 Jun 2005 15:03:40 +0000 (UTC)
markwh04@xxxxxxxxx ha escrito:
> Al.Rivero@xxxxxxxxx wrote:
> > I wonder if I could then to conclude that mesons of the third family
> > are unaffected by the chiral anomaly.
>
> The generations are the degeneracy of the charge spectrum. Therefore,
> each one is a clone in charge space and exactly the same cancellations
> applies to each. The only essential restriction requires is that a
> complete copy of the first generation appear in the 2nd and 3rd. So,
> for instance, if there's a bottom, there'd have to be a top.
Yep, and on another side, the mass of the top is very differen from the
other two generations, and I wonder if it indicates a different
underlying symmetry and thus a different anomaly.
> The constraint to remove the anomaly corresponds to Tr(gamma^5 Y_a
> {Y_b,Y_c}) = 0, where the Y's are the gauge generators.
>
> The SU(2) and SU(3) generators automatically fall through correctly; as
> does anything else that is parity-symmetric. The only culprit is the
> hypercharge Y.
>
> (...)
>
> In other words, the anomaly is basically forcing a parity symmetric
> algebra to re-emerge.
...
> It's of interest to note that the charge generator Q (electric charge)
> which remains after symmetry breaking will then take on the revealing
> form
> Q = I3 + Y = I3 + I3_R + G;
> i.e., a parity symmetric residue of a possible SU(2)_R x SU(2)_L.
...
But, can your arguments be used to show that the chiral anomaly
reponsible of pion decay emerges from the gauge anomaly of the stardard
model?
.
- References:
- Weinberg on the anomaly
- From: Al . Rivero
- Re: Weinberg on the anomaly
- From: markwh04
- Weinberg on the anomaly
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