Confusion with the Gordon identity

[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

 

[Dr.AbeNikIanEdL]

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

 

[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...