Why Spinors Are Irreducible if Gamma-Traceless: Explained

[filip97]

I read this question

https://physics.stackexchange.com/q...onditions-is-a-vector-spinor-gamma-trace-free . Also I read Sexl and Urbantke book about groups. But I don't 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 ?

 

[dextercioby]

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

 

[samalkhaiat]

It may very well be the one on the SE website, though.

It is. If he could not understand the reasoning in the SE website, he may not be able to understand my answer in the following
https://www.physicsforums.com/threa...theory-from-the-ground-up.941219/post-5954706

 

[filip97]

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?

 

[Michael Price]

This a may be helpful:
https://en.m.wikipedia.org/wiki/Rarita–Schwinger_equationThere's also a blog some one from Oxford did about this - if I can find it again, I'll post the link.
EDIT
https://suchideas.com/articles/physics/quantum/rarita-schwinger/

 

[samalkhaiat]

This a may be helpful:
https://en.m.wikipedia.org/wiki/Rarita–Schwinger_equationThere's also a blog some one from Oxford did about this - if I can find it again, I'll post the link.
EDIT
https://suchideas.com/articles/physics/quantum/rarita-schwinger/

Non of your links explain the matter better and/or easier than I did in the other thread. And your second link contains wrong as well as confused statements.

 

[filip97]

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 don't clear ho we contract Dirac equation with gamma(mu). Thanks a lot !