# Confusion with the Gordon identity

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1. Feb 17, 2016

### Higgsy

For the Gordon identity

$$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}u_{s}(\textbf{p}) = \bar{u}_{s'}(\textbf{p}')[(p'+p)^{\mu} -2iS^{\mu\nu} (p'-p)_{\nu}]u_{s}(\textbf{p})$$

If I plug in $\mu$=5, what exactly does the corresponding $(p'+p)^{5}$ represent?
4 vectors can only have 4 components so is this just an exponential?

Thanks

2. Feb 17, 2016

### Dr.AbeNikIanEdL

That does not make sense. Why would you plug in $\mu = 5$, and what would that be supposed to mean?

3. Feb 17, 2016

### ChrisVer

It is a 4vector...
$( p' + p ) ^\mu = p'^\mu + p^\mu$...
the first notation is shorter...

$\mu$ is an index taking values 0,1,2,3...

Don't get confused with the $\gamma^5$... it is not $\gamma^\mu$ with $\mu=5$, but it's a different object...