# Gamma - traceless

• A

https://physics.stackexchange.com/q...onditions-is-a-vector-spinor-gamma-trace-free . Also I read Sexl and Urbantke book about groups. But I dont understand why spinors is irreducible if these are gamma-tracelees. Also I read many papers about higher spin fields in which doesn't explain and proof gamma traceless(irreducibility condition) of spinors of higher rank. Can any explain this ?

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dextercioby
Homework Helper
Perhaps if we ping @samalkhaiat , you can get an answer. :) It may very well be the one on the SE website, though.

Ok, it is clearer. But why 1/2 component carried with divergence of Dirac spinor ? (This removing ghosts ?)

samalkhaiat
Ok, it is clearer.
Is it? Then why are you asking this?
But why 1/2 component carried with divergence of Dirac spinor ?
First: $\psi^{\mu}(x)$ is a spinor-vector field. It describes spin-3/2 particle and its anti-particle. It is NOT a Dirac spinor (Dirac spinor field describes spin-1/2 particle and its anti-particle).
Second: The divergence of $\psi^{\mu}(x)$ IS a Dirac spinor because (as I have already explained in the other thread) $\partial_{\mu}\psi^{\mu}$ satisfies the Dirac equation. In other words, the field $\psi (x) \equiv \partial_{\mu}\psi^{\mu}(x)$ represents one of the two spin-1/2 components of the spinor-vector field $\psi^{\mu}(x)$. All of this was explained in the other thread.
(This removing ghosts ?)
Which ghosts are these?

filip97
Can we raising and lowering indices of mwtric spinor with 2-contravariant or 2-covariant with metric tensor ? I think that we can do this with sigma(mu,nu) this write in Sexl Urbantke book of group representation. I was post this question because dont clear ho we contract Dirac equation with gamma(mu). Thanks a lot !!!